A recent law review article on the topic covers this question exhaustively.
Already in Anglo-Saxon times, England condemned polygamy as a serious
moral offense. But until 1604, it was left to church courts to punish
polygamists using spiritual punishments. In 1604, however, Parliament
enacted the Polygamy Act that made polygamy a capital crime,
punishable by secular courts. Both individual victims of desertion or
double marriage as well as church or state officials could initiate
indictment of parties for polygamy. Other interested parties also had
standing to press polygamy claims.
Thousands of polygamy cases came before the criminal tribunals of
England, not least the famous Old Bailey, which heard more than 500
such polygamy cases under the 1604 Act.
Convicted parties faced punishments ranging from fines and short
imprisonment, to transportation to a penal colony or execution orders,
though almost all those convicted for a capital felony successfully
pled benefit of clergy. The vast majority of polygamy cases were
brought against men, and they were punished far more severely than
women if convicted. The 1604 Polygamy Act -- while eventually
replaced by Acts of Parliament in 1828 and 1861 that made felony a
non-capital crime -- was a model for the common law world.