The Government will come under renewed pressure tomorrow to allow parents the right to reject the controversial MMR vaccine in favour of three single jabs.

Conservative MP Julie Kirkbride, who decided against giving her infant son, Angus, the MMR jab, is to introduce a Bill in Parliament calling on ministers to allow parents to choose.

Ms Kirkbride has been at odds with the Prime Minister since she demanded that Tony Blair publicly release medical details of his son, Leo.

Her cause is backed by a majority of Tory MPs, Labour backbenchers Dr Ian Gibson and Lindsay Hoyle, and many concerned parents.

Public fears were aroused by medical evidence, dismissed by the Government, that the MMR might be a cause of autism or bowel disorders in children.

Ministers and Department of Health advisers insist the vaccine is safe. But 2,000 parents are suing the department with claims that their children have been adversely affected by the MMR jab.

Ms Kirkbride's 10-minute rule Bill, which is unlikely to get the Government support it needs to pass the Commons, calls for single vaccines to be available free on the NHS.

The Secretary of State for Health, Alan Milburn, told The Independent on Sunday that the Government was still determined to "win the hearts and minds of people on this".

The Government has avoided a national advertising campaign, choosing instead a more personal approach – trying to allay parents fears by talking to them, and opening up ways they can talk to experts and get information on the issue from the internet.

"After all the kerfuffle, 17 out of 20 parents are choosing MMR for their children, because it's got a proven track record of success, not only on safety grounds but also because it saves children's lives," Mr Milburn said. "We have to convince doubters that actually it is the best way forward for the public's health."

But Ms Kirkbride and her supporters argue that giving parents the choice would increase inoculation levels and reduce the chances of children contracting the dangerous diseases measles, mumps and rubella.

"I strongly believe in the right of parents to choose what they believe is in the interests of their child," Ms Kirkbride said. "Ministers cannot bully parents into having the MMR if they don't want it and the only way we will see vaccination rates going up again in Britain is if we allow parents choice."

She pointed out that she had a lot more support outside Parliament – 80 per cent of people in the latest opinion polls said parents should be given the choice – than in the House of Commons. Her high-profile supporters include Lauren Booth, Cherie Blair's half-sister, who publicly declared that she would not give her daughter, Alexandra, the MMR vaccine.