Nearly 1,000 men are living legally with multiple wives in Britain, having tied the knot in countries that authorise such arrangements.
Britain continues to recognise polygamous marriages if they have taken place in countries that allow such partnerships to exist. Pakistan, Nigeria and India are cited as examples of such countries.
The Times has learned from the Department for Work and Pensions that there are fewer than 1,000 valid polygamous marriages in the UK. Ministers also insist that very few of these are claiming a state benefit.
"Because of the small numbers concerned, our IT systems do not specifically record such information," a statement added.
But Humphrey Malins, founder of the Immigration Advisory Service, has accused the government of losing its grip on the issue.
"This is quite clearly exploitation of women," he added.
Mr Malins has told the Times that he is even more concerned about the number of unrecognised multiple marriages, many of which leave women in a precarious situation.
"I've not been able to find out from the government what the extent of the problem is," he said. "It's a very serious issue."