After a 90-minute working session in the Cabinet room at Number 10 the Liberal Democrat leader said: "Building on the momentum of the referendums in Scotland and in Wales, we are modernising Britain.
"This is about opening a path for a more modern style of politics. We have had a very constructive meeting and we look forward to building on that so we can work together to modernise Britain's constitution in the future."
With the meeting bound by the confidentiality that surrounds all Cabinet discussion, Mr Ashdown and his four parliamentary colleagues refused to go into detail about the substance of the talks, but the Prime Minister's office said the main constitutional issues had been examined.
"In particular, they acknowledged the beneficial effects of working closely together on the referendum campaigns and agreed to co-operate closely on the legislation which follows," a spokesman said.
Members of the committee recognise that cross-party co-operation will help avoid some of the problems associated with the debacle over the failure of Labour's devolution package in the 1970s.
The meeting also included discussion about the incorporation into UK law of the European Convention on Human Rights, the 1999 Euro-elections - which will be the first national elections to be held under proportional representation - and the creation of a commission to consider an agreed option on PR for Westminster parliamentary elections, to be set up this autumn.
That commission will report within a year, and there will be a referendum offering the voters PR for general elections - to be staged before the next election. Completion of the process could then be one of the key offers made to voters by the alliance at the next election.Reuse content