If the purported husband (PH) has not attempted to enter the UK under false pretenses, and has not submitted documents containing false statements to the UK government, it is hard to see how he might be charged with a crime by the UK in connection with the invalid marriage.
But since the PH is now said to have submitted an application for entry clearance based on the bigamous marriage, a marriage that it appears that he knew or should have known was invalid, he has submitted an official document based on a false statement. That is presumably an offense under UK law, and may well affect the PH's future immigration treatment.
If the deceived wife has not knowingly made false statements to the UK government, it is hard to see how she would be charged in the UK. She would be wise to promptly inform the UK government that the marriage was invalid, to withdraw any statements or applications based on its validity, and to take legal steps to correct the record so that the marriage does not show as valid. This might be by annulment or some other procedure, probably depending on the law in the Bahamas where the purported marriage took place. (Under chapter 125, section 21(b) a prior marriage is valid grounds for an annulment or decree of nullity.) She might also want to notify the US authorities.
The purported husband might have been guilty of bigamy in the Bahamas, depending on just how their law is written. Whether the authorities there will seek to extradite and prosecute him one cannot say.