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The campaigning parent has given her support to Heidi Crowter from Coventry who is challenging abortion law at the UK High Court.
Ms Crowter, 26, is taking legal action against the UK Government with the support of Maire Lea-Wilson, 33 whose son Aidan also has the condition.
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The pair are challenging legislation that allows abortions up to birth for babies with Down’s syndrome, which they say is discriminatory.
Ms Murray has backed this position saying the current law promotes inequality.
She said: “By stating that disability is grounds for termination, section 1(1)(d) of the Abortion Act, promotes inequality.
“The provision in the Abortion Act harks back to a time when we thought it was better for people with disabilities not to be part of our society. We’re a far more progressive society now, we realise that diversity is healthy, and all of our laws should reflect that.”
Currently, there is a general 24-week time limit to have an abortion in Scotland, England and Wales. But terminations can be permitted up until birth if there is “a substantial risk that if the child were born it would suffer from such physical or mental abnormalities as to be seriously handicapped.” This criteria includes Down’s syndrome.
Lawyers representing Ms Crowter and Ms Lea-Wilson will argue that the law as it stands is unlawfully discriminatory, in a court case starting yesterday.
Ms Murray described Ms Crowter as an “inspiration” who has bravely gone where more powerful people would be scared to go.
She said: “For too long people with Down’s syndrome have been marginalised and excluded from society - but the advent of equality law means that this should no longer the case and these equality ideas should be embedded in every law, including abortion law.
“Many people thought that the law needed to be changed but Heidi is the one who’s taken up the fight. Heidi has led and inspired many people and she has done it in her own inimitable way.
“Heidi has brought this case, she has gone where other people, more powerful people, were scared to go.”