The Government accepted the proposal as it published details of a new draft Bill on political funding, expected to be included in the Queen's Speech this autumn.
The Bill will also introduce a pounds 20m limit on general election spending and compulsory disclosure of all donations of more than pounds 5,000 nationally, and pounds 1,000 locally. It will also ban foreign and anonymous gifts to political bodies.
Tony Blair has promised a referendum over joining the single currency, and the poll is likely to be one of the hardest ever fought in Britain.
Mr Straw told the Commons: "As the [Neill] committee indicates, a government is almost bound to be closely engaged in the subject matter of a referendum. There is, however, a point where the Government should step back and leave it to the political parties and other campaign groups to make their case to the electorate."
Under plans designed to clean up political funding and introduce a new transparency into the process, ministers also agreed that parties should keep public registers of all donations over pounds 5,000.
There will also be restrictions on candidates who want to stand for posts such as the mayor of London. Candidates in such internal party elections will have to disclose all donations over pounds 5,000.
But ministers rejected one key recommendation of Lord Neill's committee, that donations under pounds 500 should qualify for tax relief.
They said that the proposal, designed to reduce parties' dependence on wealthy individuals like the treasurer of the Conservative Party, Michael Ashcroft, would cost pounds 4m or pounds 5m a year and would be "amount to general state aid by another route".
The ministers accepted 98 of the Neill committee's 100 recommendations - although they also cut a proposed maximum forfeit for accepting banned donations from 10 times the amount of the gift to an amount equal to the gift.
Political parties will receive extra state funding. They have already seen an expansion of "short money" paid to opposition groups from pounds 1.5m to pounds 3.37m for the Conservatives and from pounds 316,000 to pounds 1.08m for the Liberal Democrats.
Corresponding sums will be paid in Scotland, where the nationalists will receive pounds 175,000.
There will also be a new, pounds 2m policy development fund for all parties. Free mailings will also be extended to elections to the Scottish Parliament and the Welsh Assembly.
Ministers went further than Lord Neill in one area, imposing spending limits of pounds 5m for the main opposing groups in referendums and limits of pounds 500,000 for other groups in such a campaign. The two main groups will each receive a maximum of pounds 600,000 public funding.
One Tory dismissed the Government's political funding proposals as "an act of reprisal" and others claimed they were unfair because plans to ban blind trusts such as those used to fund Labour before 1997 were not in the draft Bill.
Defending the proposals, Mr Straw said they gave politicians a chance to make significant improvements to a vital area of Britain's national life.
"For too long, public confidence in the political system has been undermined by the absence of clear, fair and open state controls on how political parties are funded," the Home Secretary said.Reuse content