Campaigners today vowed to re-open the fight to tighten up the abortion laws after a third Cabinet minister came out in favour of cutting the current 24-week limit.

Home Secretary Theresa May said she believed there was scope to reduce the limit on when a termination can take place, to 20 weeks into a pregnancy.

Earlier the new Health Secretary Jeremy Hunt went even further, saying he believed the limit should be cut to 12 weeks - half the present maximum.

With Culture Secretary Maria Miller, who is also the minister for women, having already said that she would like a 20 week limit, campaigners signalled a new push in Parliament to change the law.

However the move horrified women's rights activists who warned that a reduction could effectively prevent testing for conditions such as Down's syndrome.

Mrs May stressed that all the ministers concerned were expressing personal views and that the Government had no plans to review the 24-week time limit.

"The Government has no plans to change the law on this, we have got no plans to reduce the abortion limit," she told the BBC Radio 4 Today programme.

She added, however: "I think there is scope for some reduction. My own view is probably a reduction to 20 weeks. That is a personal view of mine."

But it was the intervention of Mr Hunt, who was promoted to Health by David Cameron in last month's Cabinet reshuffle, which galvanised campaigners pressing for a lower limit.

"Everyone looks at the evidence and comes to a view about when they think that moment is and my view is that 12 weeks is the right point for it," he told The Times.

"It is just my view about that incredibly difficult question about the moment that we should deem life to start."

He added: "I don't think the reason I have that view is for religious reasons."

His comments, on the eve of the Conservative Party conference in Birmingham, were warmly welcomed by Tory backbencher Daniel Kawcynski.

"There are Members of Parliament of all parties who feel very strongly that we need to change the limit," he told the Today programme.

"The Health Secretary coming out in favour of re-igniting this debate will galvanise the caucus that exists in Parliament, cross-party, on this issue.

"There will be many of us who will never stop campaigning to reduce the limit. For as long as I am a Member of Parliament, I will never give up this fight."

However Professor Wendy Savage, a gynaecologist and campaigner on women's rights, expressed alarm at the prospect of another move to reduce the limit following the defeat in Parliament of the last attempt in 2008.

"The number of abortions that take place over 20 weeks is very small. Of those a considerable proportion are of foetuses which have got a congenital abnormality," she told Today.

"I think the majority of the population think that if somebody has got a foetus that, if born, will have a severe disability they should have the right to choose whether or not to continue with that pregnancy."

Diane Abbott, who is Labour's shadow public health minister, accused ministers of "playing politics with people's lives", insisting there was no justification for a reduction in the present limit.

"We're seeing a sustained ideological attack on the science, and the rights that British women and families have fought for," she said.

"There is no evidence to support a reduction in the abortion time limit and this view is supported across the medical profession.

"Late abortion only affects a small number of women, who are often in extremely challenging circumstances."

Mr Cameron said he did not agree with Mr Hunt's position, but added that he was entitled to his opinion.

"He is a Member of Parliament, he is absolutely entitled to hold an individual view, a view of conscience and on this issue all Members of Parliament - Prime Ministers, Health Secretaries, everybody - has to vote according to their consciences.

"They are totally entitled to hold that view but people need to know the Government has got no plans to bring forward any legislation in this area and any vote that does happen will be a free vote," he said.

The Prime Minister added that he was in favour of a smaller decrease in the abortion limit.

"I personally have voted for a modest reduction from the current limit of 24 weeks because I think there are some medical arguments for that. But I don't agree with the 12-week limit and that's not the Government's policy," he said.