Hundreds of women demonstrators clashed with police in and around the British Parliament building today during protests against legislation that would tighten Britain's relatively liberal abortion law.

While an emotional debate on the bill took place inside a packed House of Commons chamber, the pro-abortion protesters outside waved their fists in the air and chanted: "Not the church, not the state, we must decide our fate."

A dozen shouting demonstrators got into the public gallery above the Commons floor and unfurled a pro-abortion banner before being pulled out by the morning-coated doorkeepers, one of whom was bitten on the hand.

About 75 other demonstrators trying to enter the building were trapped in a vestibule before being dragged and shoved back outside by scores of police who pushed through the rest of the huge crowd outside, scattering women and children. Protest leaders said some children and a pregnant woman were knocked down in the police rush.

Some of the women then tried to stop traffic in the busy street but as police reinforcements arrived they and the rest of the demonstrators retreated. They then regrouped for a scheduled early evening torchlight march from Parliament past the law courts and through Fleet Street, where Britain's national newspapers are published.The march was noisy but peaceful.

The bill the women were protesting so vociferously against was widely believed to be doomed to defeat or emasculation in Parliament by opponents using stalling tactics and offering an endless string of amendments. It was introduced by John Corrie, a Conservative from Scotland, rather than the government and therefore lacks government backing to protect it from such tactics.

Corrie's bill would drastically amend Britain's 1967 liberalization of abortion law that allows abortions to be performed during the first 28 weeks of pregnancy when physicians decide risk to the woman's physical or mental health would be greater if the pregnancy continued.

Physicians, family planning organizations and abortion clinics have interpreted the law liberally. The number of abortions in Britain has increased from about 20,000 each year before 1967 to about 130,000 now, including about 30,000 women who come here from nearby countries with stricter abortion laws.

As in the United States and elsewhere abortion has become an emotional issue here with frequent, large public demonstrations and persistent pressure on Parliament. There have been six previous attempts to change the law.

Corrie's bill would reduce the outside time limit for abortions from 28 to 20 weeks of pregnancy unless the child was likely to be born handicapped or the mother's life was endangered. It would also tighten the criteria for performing abortions within those 20 weeks and place restrictions on clinics and physicians that would reduce the number of abortions by half or more.

The bill, which is opposed by physicians' groups, has divided Parliament. Some of its opponents and Prime Minis ter Margaret Thatcher's minister of health, Dr. Gerard Vaughan, have said they would agree to reduce the time limit from 28 to 24 weeks if the law was not substantially changed otherwise.

The author of the controversial 1967 law, Liberal Party leader David Steel, said he would agree to a 24-week limit because advances in medical science have made it possible to keep older fetuses alive. "When one looks at 24 week," he said, "at this stage of gestation only a tiny minority of fetuses would be capable of separate existence."

But this is just one of many amendments to Corrie's bill that threaten to take up all of its limited time for debate in the weeks ahead and enable opponents to filibuster it to death, if not vote it down outright.