The Bill is to be one of 26 expected in today's Queen's Speech programme for the new session of Parliament.
Welcomed at No 10 by Cherie Booth, 14 parents of some of the Dunblane victims were given a guided tour by her before meeting Mr Blair, Jack Straw, the Home Secretary, and Donald Dewar, Secretary of State for Scotland, who briefed them on the four-clause Bill which will get a free vote of Labour MPs in the Commons.
The Bill will not only ban all handguns, including the .22 guns exempted by the Conservative government legislation, but will also revoke the possibility of owners holding their guns on club premises.
While the legislation will go through the Commons without difficulty, House of Lords "backwoodsmen" are expected to put up stiff resistance, and could even defeat it in the Upper House.
The Prime Minister urged the parents' group to mobilise their campaign against the gun lobby, but he said that even if the Lords did stop the Bill in the forthcoming parliamentary session, he would bring it back again in the next session - allowing it to be forced through against the will of the Lords.
Certainly, if the hereditary peerage does block the Bill, it could be their last act of defiance - and would most certainly be used as ammunition by the Government to divest them of their power to sit and vote in a reformed Lords chamber.
Opening the debate on the Queen's Speech this afternoon, following the traditional State Opening of Parliament, Mr Blair will tell the Commons: "We are the people's government".
The themes of the legislative programme will be the one nation desire to bring the country together, after years of Tory division, and equipping it for the future, with two Education Bills to be at the heart of the speech.
The programme will be heavy, comparing with only 15 Bills in John Major's 1992 Queen's Speech, and there will also be three White Papers, including one on freedom of information.
The Prime Minister will say today that the government mandate is clear; to modernise what is outdated, and to make fair what has been unjust, irrespective of dogma and doctrine, without fear or favour.
Other measures expected, apart from the core pledges on crime and disorder, health, education, and devolution, will include some social security reform, the reinstatement of an asylum appeals process, and action on restrictive practices.
The Prime Minister's office said that Boris Yeltsin, the President of Russia, had called Mr Blair for a 20-minute conversation about Anglo- Russian relations yesterday.
The two men have not met before, but they are expected to have further talks at a Nato-treaty signing ceremony in Paris, and again at this month's Group of Seven/Eight developed nations' meeting, in Denver, Colorado, at the end of this month.Reuse content