Peers clashed today over the role of Sharia law tribunals as they backed measures aimed at toughening rules on sex discrimination and domestic violence.
Independent crossbencher Baroness Cox warned about the "suffering of women oppressed by religiously sanctioned gender discrimination in this country".
And she hit out at a "rapidly developing quasi-legal system, which undermines the fundamental principle of one law for all".
Lady Cox said her move to tackle this in the Arbitration and Mediation Services (Equality) Bill was backed by many Muslims and could apply to discrimination by other faiths.
She denied being "anti-Muslim" insisting she wanted Muslim women to enjoy their full legal rights under British law.
But the first female Muslim peer, Baroness Uddin, said the bid to change the law would be seen, outside the House, as "another assault on Muslims".
Lady Uddin said the way forward was for the Government to look at the issue in partnership with the affected communities and womens' groups.
"No laws should supersede the laws of the land where citizens reside and coercion to religious law is unacceptable," she said.
Lady Cox said problems often arose because many women believed Sharia courts were "real courts" and they did not have other rights under English law or were "pressured" not to seek those rights.
She said many such women lived in fear and dare not speak out about problems of domestic violence and gender discrimination.
Her Bill did not interfere with the theological affairs of religious groups and if people wanted to submit voluntarily to the rulings of any body they were free to do so.
But it would make it a criminal offence "falsely to claim legal jurisdiction" and make it easier to have discriminatory rulings overturned, as well as strengthening protections against domestic violence.
"I don't believe we can continue with the present situation where so many women are suffering from gender discrimination in our country today, in ways that would make the suffragette movement turn in their graves."