The Bill could give the security forces and the police the power to begin a sweep next weekend of IRA renegades responsible for the Omagh bombing, fulfilling the threat by Mo Mowlam, the Secretary of State for Northern Ireland, to take them "off the streets". But there is growing anxiety at Westminster over the way the legislation is being introduced.
The "catch-all" nature of one of the key clauses of the Bill is a cause for concern among Labour MPs, including Kevin McNamara, a former Labour Northern Ireland spokesman, who is threatening to table amendments.
John Major, the former prime minister, who promoted the peace process, has so far backed Tony Blair's strategy with regard to the Good Friday peace deal, but is planning to raise critical questions about the haste with which the Government is planning to introduce the new laws.
The Bill would allow the courts to convict a person alleged to be a member of any banned terrorist group, such as the Real IRA, on the evidence of one police officer of the rank of superintendent or higher, without corroborative evidence.
It would also allow courts to draw inferences of guilt from a refusal to answer questions about the membership of proscribed groups.
There is likely to be more controversy over the provisions of the Bill that cover international terrorism, in the wake of the attacks on the American embassies by Islamic extremists. At the request of the Egyptian government, ministers are to include a clause to create a new criminal offence of conspiracy within the UK to commit any offence outside the UK.
A Downing Street source admitted that the parliamentary draftsmen had found it impossible to draw the legislation tightly to target only terrorists. "It was impossible to distinguish between a bank robbery and a bank robbery to raise money for terrorism," said the source.
Underlining the wider scope of the Bill, it is being regarded as Home Office legislation, and therefore will be presented by the Home Secretary, Jack Straw, rather than a Northern Ireland minister. A wider review of anti-terror laws is due in the autumn.
Officials are discussing this weekend whether it should include measures to allow phone-taps to be used in evidence in British courts for the first time.
Mr Blair will be discussing the package with ministers at Chequers on Tuesday before the Bill goes through its Commons stages on Wednesday. It will go to the Lords on Thursday and if there are any amendments, the Commons will be asked briefly to sit again before the legislation is given Royal Assent on Thursday night.
Mo Mowlam will miss the vote. She will be in Ulster hosting a conference for women with Hillary Clinton. Bill Clinton will arrive in Belfast on Thursday from Moscow and it is expected that the Prime Minister will join him in a visit to the scene of the Omagh bombing to underline the condemnation of the US administration for the IRA breakaway group.
Mr Clinton is expected to say that the group will be denied access to fund-raising in the United States, before flying to Dublin for talks with the Irish Prime Minister, Bertie Ahern.