Heralded by a leading historian as "big time", the decision could help the drive to proportional representation for Commons elections, which some senior politicians believe could crack a brittle Conservative Party.
One well-placed source told The Independent the innovation could form a chapter of its own in a future history on "The Strange Death of Conservative Britain".
While the new consultative Cabinet committee falls short of coalition or pact, it will give the Liberal Democrats a unique chance to make a formal, closed-door contribution to legislation across a broad range of policy. It is the more significant because Mr Blair has a Commons majority of 180.
Diehard traditionalists in both parties were last night hostile to the move, but Mr Ashdown said it could contribute towards a more "rational, mature and civilised style of politics... the real beginning of a different style from which we all benefit".
The decision ends a process of discussion that has been going on since before the election. It was raised by the Prime Minister at his first Cabinet meeting in May and discussions have been taking place between Mr Blair and Mr Ashdown ever since, including talks en route from the Hong Kong handover.
The fact that the secret was kept says much for the trust that exists between the two leaders. Mr Blair will chair the committee and there will be a "heavyweight" membership, though there was uncertainty last night as to whether John Prescott, the Deputy Prime Minister, or Gordon Brown, Chancellor of the Exchequer, would want to serve.
Robin Cook, the Foreign Secretary, helped to create a joint constitutional platform with the Liberal Democrats' Robert Maclennan before the election, and that programme will form an initial agenda for the new committee.
Peter Mandelson, Minister without Portfolio and Mr Blair's most trusted Whitehall leg-man, is also expected to be a member.
In a book he co-authored last year, The Blair Revolution, Mr Mandelson wrote: "A government with its sights on the long-term needs to have the broadest possible political base from which to obtain consent for change that will last, to overcome short-run unpopularity, and to govern in the national interest." That meant a lot of "hard thought" about relations with the Liberal Democrats.
Peter Hennessy, Professor of History at London University and an expert on Cabinet government, said last night: "This is big time. It is very significant. The creation of a Cabinet committee gives the relationship status and formality, and puts them on the inside track." It also suggested a more open, less command-control, leadership.
While Opposition leaders have been invited to attend Cabinet committees in the past, subjects for discussion have always been specific, as when Churchill and some senior Tories were invited by Attlee to attend a Cabinet committee on defence in 1949.
The form and style of the new committee is unprecedented in British politics.
Although his office said last night that it was very much Mr Blair's own idea, it marks a personal triumph for Mr Ashdown, who has always sought a more consensual style.
But as he said yesterday, the two parties would maintain their distinct identities. Mr Ashdown pointed out that Malcolm Bruce, the Liberal Democrats' Treasury spokesman, had been attending a select committee hearing yesterday, in which he was repeating his attack on spending cuts.
To underline that message, Mr Bruce's office later issued a series of Commons replies showing that real terms health spending would be pounds 66,595m between 1997-99 under Labour, compared with pounds 66,596m under Kenneth Clarke's plans - a cut of pounds 1m.
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