Just to make a distinction... Henry VIII never actually divorced any of his wives.
Anyone in Henry's realm could seek an annulment. But the grounds for such were fairly difficult to prove, and courts were reluctant to grant them in general. Apparently only a handful of annulments a year were granted in all of England. The most common form of legal action was a type of legal separation called "divorce from bread and board." That allowed the spouses to set up separate homes, but they didn't allow the parties to remarry. Even that was only granted upon proof of adultery or extreme cruelty. Divorce itself required an act of parliament and was almost never granted, and certainly wasn't granted to the common folk. As far as I can tell there was no change in any of the laws or the application of the laws during Henry's reign. Both annulments and separations remained very rare. In Tudor England it really was "Til death do you part" unless one was the king.
Sources. Martin Ingram, Church Courts, Sex and Marriage Lawrence Stone, The Family, Sex and Marriage in England 1500-1800
The premise of your question is wrong in two ways. First, as /u/QuickSpore pointed out, none of Henry VIII's wives were actually divorced (annulments, declared invalid, execution, etc). But second, and more importantly, divorce was never outlawed in England. Yes, it was rare, but by no means illegal.
According to the British National Archives, reasons for divorce in the middle ages included:
Impotency
If either partner had made a previous monastic vow
Non-consummation
If either party had a pre-arranged marriage contract - though this would make the second marriage invalid and not technically be a divorce
If a party was "too young" to be married (child marriages did happen, but not as often as is commonly believed, and the practice was even less common among commoners)
If the marriage was done in secret
If force was used to obtain the marriage
Marriages entered under false pretenses (Think The Return of Martin Guerre)