The idea of a formal "mourning period" after the death of a spouse--especially the Victorian one with various stages (with colour-coordinated clothing) --is largely a post-medieval concept, as well as a class-linked concept. Societal attitudes about the remarriage of widows were considerably different in the medieval period, and the church and secular society had different focuses. Let's take a look at those.
First, from the standpoint of the Church: Many of the early Christian writers were iffy about the concept of the remarriage of widows, although the idea that it was actually sinful and a form of adultery was discarded early. This was tied into the general idea that the ideal state that was most admirable for all (both men and women of all ages) was abstinence and chastity, the total abjuration of the "desires of the flesh" in order to contemplate the holy. Marriage was, to paraphrase Augustine, was better than burning, and he wrote, in a treatise specifically about widowhood, that it would be preferable to renounce bodily pleasures instead of spiritual ones and not remarry.
However, as the idea of marriage as a sacrament in its own right began to take primacy, with further separation between laity and clergy, this attitude did evolve considerably, contemporaneously with secular law regarding property rights. By the twelfth century, canonists did not question the legitimacy of second (or even subsequent) marriages.
However, questions of inheritance and property began to become significant points of contention regarding the remarriage of widows. A marriage that took place at the church (or at the church door, as it was done in England, as a way of making it public) was one that could be recorded in a parish register, thus providing proof for any questions of inheritance or property rights. In England, a woman's dower (that portion meant to support her for the rest of her life) was announced as part of this ceremony; traditionally, it was 1/3 of her husband's estate unless otherwise specified. A wealthy widow would also usually manage the affairs of any minor children until they came of age. Thus, the remarriage of high-ranking widows became a pathway to increased wealth, and lords began to both deny widows their dower and any inheritance, and to seek to control and even force the remarriage of their vassals' widows as a way to continue to control their wealth and properly. This was, famously, one of the complaints raised against King John in England, and led to two clauses in Magna Carta:

7. A widow, after the death of her husband, shall forthwith and without difficulty have her marriage portion and inheritance; nor shall she give anything for her dower, or for her marriage portion, or for the inheritance which her husband and she held on the day of the death of that husband; and she may remain in the house of her husband for forty days after his death, within which time her dower shall be assigned to her.

8. No widow shall be compelled to marry, so long as she prefers to live without a husband; provided always that she gives security not to marry without our consent, if she holds of us, or without the consent of the lord of whom she holds, if she holds of another.

So in England, the standard became that lords were not to force widows to remarry against their wills, but they needed to ask permission to do so of their own accord (generally paying a fine for obtaining that permission). Church courts were also generally willing to annul marriages of widows where coercion could be proved. But the focus at this point is now becoming not the propriety of second marriages from a religious standpoint, but instead the inheritance implications. And around the 13th century, there are occasional mentions, for the first time, in secular law, of mandatory mourning periods between the death of a spouse and remarriage--and these are made completely in the context of inheritance law.

Bringing things back around to Brother Cadfael, the books (and TV series) are set in the 12th century, before Magna Carta but in an era in which the attempt to obtain or control wealth through the marriage to or the control of wealthy widows was definitely a growing concern. There was no set mourning period at this point. Based on what I have mentioned, the objection to the remarriage of a wealthy widow (particularly a hasty one) would be less about propriety and more about potential predatory suitors aiming to get control of her property (and that of any minor children). And because there is a class component to this, the remarriage of a widow without significant property simply would not be an issue at all--in fact, it would be encouraged, as such widows without means of support often had to either earn their own keep or rely on relatives, or in extreme cases, be forced into begging or at the mercy of (usually religious) charities who might take them in in exchange for labour. These women would have been encouraged to remarry as quickly as possible if they were able.

(Source: James A. Brundage, Law, Sex, and Christian Society in Medieval Europe)