A fresh attempt to curb the powers of Sharia courts over vulnerable Muslim women has been launched in the House of Lords.

Independent crossbencher Baroness Cox said her aim was to tackle the "suffering of women oppressed" by religiously linked gender discrimination.

She also spoke out against a "rapidly developing alternative quasi-legal system which undermines the fundamental principle of one law for all".

Lady Cox said problems were escalating and finding a solution was ever more urgent in areas like women's rights in marriage and divorce under Sharia law.

"We must not condone situations where rulings are applied which are fundamentally incompatible with the laws, values, principles and policies of our country."

The operation of Sharia law principles in the UK must not be allowed to undermine the rights of women and the rule of law, she said.

Opening second reading of her Arbitration and Mediation Services (Equality) Bill, which aims to close loopholes in equality laws, Lady Cox said: "Muslim women are today suffering in ways in which would make suffragettes turn in their graves.

"Many of them see the proposals in this Bill as a lifeline.

"It would provide some much needed help and show vulnerable British Muslim women that their concerns are being taken seriously rather than ignored in the name of political correctness and multi-culturalism."

Sharia courts, or councils, settle disputes over issues like marriage using Islamic law.

Several previous attempts by Lady Cox to change the law in this area have failed due to lack of Parliamentary time and government support.

The former Archbishop of Canterbury, Lord Carey of Clifton, backing the Bill, said: "Whenever a minority of Sharia courts exist to trump civil law we must correct abuses and do this by strengthening existing laws to ensure Muslim women have the same rights as men."

The independent crossbencher said it was easy to take freedom and tolerance for granted. He warned that the traditions of new citizens to the UK "may collide sharply with the resident nation and raise questions about compatibility".

Such was the case with "marital relationships when they appear before Sharia courts", Lord Carey said.

Muslim women "trapped in bad marriages with intimidation and threats whenever they tried to free themselves" must be able to rely on Parliament to "rescue" them.

Labour's Baroness Donaghy, a former chairwoman of Acas, also supporting the legislation, said the majority of women married under Sharia law were not aware that this did not give them legal rights under UK law on marriage, placing them at a potential disadvantage.

Tory former lord chancellor Lord Mackay of Clashfern said it was easy to put the issue off but the urgency of the situation merited Government action at an early date.

Independent crossbencher Lord Green of Deddington, chairman of Migration Watch UK, said there could be only one law in Britain and equality for men and women under it.

"The problem is the growing body of evidence that arbitration by Sharia courts does in practice discriminate against women in a manner that is unacceptable in British society."