There's an implication of a misconception in your question that I think is addressed by the appendix to William Page Wood's 1859 speech on the topic:

The state of our law is singularly misunderstood, not only "out of doors," but by many members of Parliament. It is supposed that because the marriage with a wife's sister was voidable only, and not void until Lord Lyndhurst's Act, there was a species of half sanction to such unions. Now, the fact is, that no such marriage was ever in the smallest degree sanctioned; but the Courts of Common Law would not allow any proceeding in the Ecclesiastical Court to set them aside after the death of either party, so that after the death of husband or wife there was no mode of obtaining a judicial decision, and of course all marriages actually solemnized are good till such sentence is given. The best mode of making this understood is to call attention to the case of marriage with a man's own sister or mother, being in precisely the same position, and in the same sense voidable only, not void.

That is, while the 1835 act made it illegal to contract such a marriage, it had always been considered invalid under English common law for a man to marry the sister of his wife - and for a man to marry his brother's wife. It's just that it was previously more like grounds for annulment, someone would have to say, "hey, by the way, judge, my marriage was made on an illegitimate basis, please invalidate it," if they wanted to end it. After the act - or, actually, in Scotland from 1567 on - it simply couldn't happen/wasn't considered a real marriage. Ginger Frost cites the specific 1859 case of Fenton v. Livingstone in Living in Sin: Cohabiting as Husband and Wife in Nineteenth-Century England: the first wife of Thurstanus Livingstone (yes) died and in 1808 he married her sister, subsequently having a son with her; in 1832, his second wife died without ever going to court to have the marriage voided. After Livingstone died, his son inherited land from him in England and Scotland, but the Scottish courts refused to allow him his inheritance because, by their standards, his parents had never been married and he was illegitimate.

The basis for the prohibition against these kinds of marriages was the Bible, actually. Leviticus says that a man may not marry his sister, and in marrying a man and woman were considered "one flesh", so therefore a wife's sister and a husband's brother were as close to you as your own sister or brother from birth. It was as incestuous to marry them as it would be to marry your own sibling or parent. And there was concern about incest in general in Victorian England, although it was nearly always phrased to be about patronizingly looking down on the foibles and sins of the poor. For instance, there was an idea that incestuous sibling behavior was encouraged and made common by the fact that poor families were crushed into small apartments together - something that obviously wouldn't happen to the middle and upper classes, so therefore we don't need to think of them ever practicing sibling incest (or abuse). Investigative reformers also found that men pursued their wives' sisters even while their wives were alive, particularly in those overcrowded conditions. Some took it as a given that working-class men whose wives died would take in her sister to help them with the house and children, and that likewise, the closeness of the small house would encourage them to have sex, which was a problem from both the incest angle and a premarital sex angle. In Bracebridge Hemyngs's (yes) "Extra Volume" of London Labour and the London Poor (1861), while he's sympathetic to people in this situation and opposed the ban so that they could marry, he still calls it "cohabitant prostitution".

However, the simple fact is that studies of the period showed that it was overwhelmingly middle-class men who wanted to incestuously marry their wives' sisters. Supporters of the ban, like William Page Wood, could point out that Hemyngs's patronizing concern for the poor was on very shaky ground, and that it was important to guard the morals of all England, including the corrupted middle- and upper-class families - but the reason there was so much debate over it in Parliament between 1835 and 1907 is that quite a lot of unstigmatized, affluent, non-working-class widowers wanted to marry their sisters-in-law. (And in fact, a large number of these marriages still occurred between 1835 and 1907 despite the ban, the people involved typically getting around the law by traveling abroad to do it.) At the same time, marrying the wife of your deceased brother was still seen as incredibly taboo, so taboo that it did not need to be included in the 1835 act or debated in the halls of government. The debate over the ban works to conceal the complete acceptance to the reciprocal cultural prohibition.

In 1835 Lord Chancellor Lyndhurst introduced the bill to correct an earlier ambiguity in the law. The existing law about marriages within "prohibited degrees" (so family and family in law, as well as the sister of your deceased wife) was based on a law from 1533, under Henry VIII. This law stated that a marriage within prohibited degrees could be annulled at any time by the Ecclesiastical church. Any children from the marriage would become illegitimate. Lyndhurst argued that this created insecurity and inconvenience for the married couple and their children. His special motive was to protect the seventh Duke of Beaufort, who was in such a marriage, and his son, who would inherit his estate.

To solve this issue, parliament passed an edited form of Lyndhursts bill. All marriages with a deceased wife's sister (DWSM) up to 1835 were considered valid. All such marriages from that year on were prohibited.

Starting in 1835, this bill was debated almost annually, before being finally revoked in 1907. This was reverenced in the Gilbert and Sullivan opera Iolanthe as 'pricking the annual blister'. Some years it passed the House of Commons but was stopped in the House of Lords. During these years, the issue was hotly debated in the public sphere by use of pamphlets, literature and papers. In fact, the bill was part of a much larger debate about society versus the individual, how much the law could intervene in an individual's life, and the purity of marriage. The bill was used to argue about the ability of government to legislate morality, control individual behavior, and regulate the family. In a way, the yearly debating of this bill helped Victorian society to shape and determine itself.

Obviously, being discussed over so many years, there is an incredible amount of arguments in favor and against, not all of which I'm going to name in this comment. Here are a few examples:

Arguments in favor of the bill (and against DWSM)

The Victorian era looked upon incest differently then we do. It was thought that man and wife, upon marrying, became actual family. There was no difference between blood relations and in-laws in term of nearness. Since the wife is now family, so is the sister. To then marry the sister was considered incest.

There was a big taboo on incest, and a focus on seeing the bond between brother and sister as pure and not "tainted by passion or irregular desire". The argument was that the bond between brother-in-law and sister-in-law should be similarly pure. (The article by Nancy F. Anderson goes quite extensively into the fact that incest between brothers and sisters was probably fairly common and the lines between sibling-love and romantic love were sometimes blurry. The article is quite old and arguably some theories are dated. I still want to mention it but invite you to explore this aspect on your own.)

There was a biblical argument, though through the years the passages were interpreted differently. In the early years arguments in favor of the bill cited Genesis 2: "man and wife become one flesh" and Leviticus 18:16, which prohibits to "uncover the nakedness of thy brother's wife."

By 1870, science replaced religion in the debate. It was claimed for example that sexual intercourse changes the physiological makeup of the marriage partners and makes them blood relations, which again makes the sister in law a blood relation.

Lastly, there was the fear of gliding scale effect (still very popular in current politics): if this law would be revoked, other marriages within prohibited degrees might follow. There was a fear of opening the floodgates to "unnatural" marriages.

​

There were also arguments against it:

Rich people could take their wife's sister abroad (usually Scotland) and get married there. We have examples of this happening. Poor people could not, therefore the bill was felt to discriminate. In the later 19th century, there was a strong focus on caring for the poor, by making bills, charity, banning child labor etc. So this argument fits into that sentiment.

Oftentimes unmarried sisters would already be living with a family or with a widower. Especially poorer families would not be able to afford other childcare. Poorer people lived in small quarters and often shared bedrooms. DWSM would help these people to live decently instead of in sin.

Opponents also claimed that marriage did not cause a blood-relation but only a psychological connection, which would make the marriage allowable.

The validated marriages prior to 1835 were also brought out as an argument.

​

The bill had been revoked in many of England's colonies around 1880, and its final downfall started in 1906 with the Colonial Marriage Act, which granted full inheritance rights to children from deceased wife's sister marriages from the colonies, in England. This bill paved the way for the final revoking of the Wife's Sister Bill. In 1908, a new Punishment of Incest Act took its place, but this bill only prohibited sexual relations with mothers, daughters, sisters, granddaughters. Sisters in law were not mentioned in this law.

​

An interesting note:

Vanessa Stephen, sister of Virginia Woolf, fell in love with her half-sister Stella's widower Jack Hills. There's a line in Mrs. Dalloway about how "no decent man should let his wife visit a deceased wife's sister".

​

Sources consulted & further reading:

The "Marriage with a Deceased Wife's Sister Bill" Controversy: Incest, Anxiety and the Defense of Family Purity in Victorian England, Nancy F. Anderson, Journal of British Studies, Vol. 21, No. 2 (Spring, 1982), pp. 67-86

Thomas Hardy and the deceased wife's sister marriage bill, Shanta Dutta, The Thomas Hardy Journal, Vol. 11, No. 2 (MAY 1995), pp. 61-64

Triangular Desire and the Sororal Bond: The "Deceased Wife's Sister Bill" Diane M. Chambers, Mosaic: An Interdisciplinary Critical Journal, Vol. 29, No. 1 (March 1996), pp. 19-36

Husband, Wife, and Sister: Making and Remaking the Early Victorian Family, Mary Jean Corbett, Victorian Literature and Culture, Vol. 35, No. 1 (2007), pp. 1-19

The Marriage to a Deceased Wife's Sister Narrative: A Comparison of Novels, Charlotte Frew, Law and Literature, Vol. 24, No. 2 (Summer 2012), pp. 265-291

The Annual Blister: A Sidelight on Victorian Social and Parliamentary History, Cynthia Fansler Behrman, Victorian Studies, Vol. 11, No. 4 (Jun., 1968), pp. 483-502

Public opinion on marriage with a deceased wife's sister: 1875 to 1888, From the collection: Selections - university of Manchester British Political Pamphlets Collection