Muslim men in Britain are having up to 20 children each through polygamous marriages, peers have warned.

Baroness Cox, a Christian member of House of Lords, highlighted a number of cases of sharia law being imposed on Muslim women in Britain as she introduced her arbitration and mediation services (equality) bill. The bill, which passed its second reading in the House of Lords yesterday, sought to combat the Islamic legal system and give Muslim women better protection under equality legislation.

"My Muslim friends tell me that in some communities with high polygamy and divorce rates, men may have up to 20 children each," she said as she introduced her bill.

"Clearly, youngsters growing up in dysfunctional families may be vulnerable to extremism and demography may affect democracy."

Cox gave the example of one 63-year-old man who tried to divorce his 23-year-old wife and arrange her marriage to a Pakistani man who needed a visa.

He asked a gynaecologist to "repair the hymen" of his wife so she could remarry, and stood to make £10,000 "for effecting the arrangement."

"Such shocking cases surely cannot be allowed to continue," she said. "The rights of Muslim women and the rule of law in our land must be upheld."

Muslim men in Britain, Cox revealed, divorce their wives under sharia law simply by saying or writing "I divorce you" three times.

Cox's proposals would close a loophole in the Equality Act which allows sharia law courts operating in Britian to practice sexual discrimination. The legislation would make it illegal for any arbitration tribunal to "do anything that constitutes discrimination, harassment or victimisation on grounds of sex."

According to Cox, there are around 100,000 couples in Britian living under Islamic marriage which are not recognised by English law, leaving them at a disadvantage legally.

The bill received support across the house.

"We cannot afford to go backwards and tolerate a situation where any woman is living in fear and isolation" said Baroness Donaghy, a Labour peer.

"More needs to be done. This is not confined to Sharia law or Muslim religion. These parallel laws which discriminate against women have existed and may still exist in other religions."

Lord Green of Deddington, chairman of MigrationWatch, said Britain was entirely different to Muslim countries.

"We must be prepared to insist that there can be only one law," the cross-bench peer said.

"We must get away from what I call the Rotherham complex where the authorities were so afraid of offending a minority community that they turned a blind eye to the appalling abuse of young mainly British girls."

However the government's response was not entirely welcoming. Lord Faulks, the justice minister, said he did not believe new laws were needed as there were already protections in existing legislation. As a result the bill is unlikely to be adopted as new legislation.