The constitutional commission planned by the three pro-union parties to set out changes to Scottish devolution could be operating within two months, according to those close to discussions yesterday.

A meeting in London of the so-called Scottish Six - the Scottish leaders of Labour, Conservative and LibDem at both Holyrood and Westminster - yesterday discussed the remit and membership of their planned commission. It was the second meeting for Labour's Wendy Alexander and Des Browne, LibDems Nicol Stephen and Alistair Carmichael and Conservatives Annabel Goldie and David Mundell.

There had been growing tensions between Labour and other participants over the lack of a clear commitment from UK ministers, with LibDems saying they wanted a clear statement from Scotland Secretary Des Browne.

Labour's Wendy Alexander said after yesterday's meeting: "The important message is that this commission will happen. We have a mandate from the Scottish Parliament, which the SNP's National Conversation does not have."

Scottish LibDem leader Nicol Stephen said after meeting that he was satisfied Labour is committed to this process for finding cross-party agreement on changes to devolution.

Though the statement agreed by the six leaders showed little sign of progress, the next meeting, to be held in Edinburgh in the next few weeks, is seen as crucial to deciding the remit and membership, which will include representatives of parties and civic Scotland, with the freedom to set its own timetable and consult as it chooses.

Party leaders also hope to be clearer about the contribution of the Scottish Parliament, UK Parliament and UK Government in finance and staffing for the commission. Mr Stephen said Westminster should share some of the costs, as the project is "crucial to the future of the UK".

It became clear that Mr Browne is attending in his role as leader of Scottish Labour MPs, rather than representing the UK Government.

More than 20 Scottish Labour back-bench MPs attended a briefing about the commission proposal given by Mr Browne on Monday evening, where they also discussed political strategy for the year ahead.

Holyrood voted to back the commission last month, which participants interpret as a mandate to provide official resources.

That vote was in the face of SNP opposition, as the commission's remit will rule out consideration of independence as an option, and Nationalists have warned no budget is available.

The case for Scotland remaining British was strengthened yesterday with a new poll showing support for devolution running at 57% and independence at 27%.

Annabel Goldie said: "What the majority wants is the representation we have in the Scottish Parliament, the majority of MSPs coming from parties that support the Union and, therefore, what we have to do is to address the desire of majority view in Scotland, which is to stick with devolution but make it work better."

A Scottish Government source commented that its national conversation on independence was different in being inclusive, adding: "Whatever the other parties come up in terms of more powers, they must be prepared to put that to a referendum and let the people choose the future of Scotland."