Why 323 is the magic number for supporters of the 'rainbow coalition'

The figure that the Labour architects of a "rainbow coalition" will have emblazoned on their minds is 323.

That is the number of MPs who theoretically need to assemble under an anti-Tory umbrella to command a bare majority in the House of Commons. Although the actual figure for an overall majority is 326, in practice it is 323 because the five Sinn Fein MPs will not take up their seats.

Following the election, Labour, with 258 MPs, and the Liberal Democrats, with 57 MPs, have 315 MPs between them. The Scottish National Party (SNP), with its six MPs, and Plaid Cymru, with three, would take an anti-Tory bloc to 324 MPs. But there would be resistance among senior Labour figures to any deal that would involve the SNP, their bitter foes in Scotland.

There is, however, an alternative grouping that could stumble – just – to the winning post. It would involve Labour, the Liberal Democrats, Plaid Cymru, as well as five MPs from Northern Ireland. They are three from the SDLP, Labour's sister party, one from the non-sectarian Alliance Party, the Liberal Democrats' sister party, and Dame Sylvia Hermon, the independent unionist who has traditionally leaned towards Labour.

They might also even be able to count on support from the eight Democrat Unionist Party MPs. Although the DUP might seem more natural bed fellows of the Tories, the party has had major disagreements with previous Conservative administrations, and has repeatedly said that it would do business with either party. The question of money for Northern Ireland would certainly trump any ideological considerations.

But, even without the DUP, a rainbow coalition would muster 323 MPs. To their number could be added the Greens' first MP, Caroline Lucas, whose party said she would "want to play a constructive role in fighting for electoral reform".

One cabinet minister told The Independent: "Anyone who knows the Liberal Democrats realises they won't be able to do a deal with the Tories. There will be a progressive coalition, I feel fairly confident of that. But we've got to wait for the talks with the Tories to fail."

It would be a precarious arrangement, which would be imperilled by the death of an MP, a missed flight to London or a backbencher refusing to toe the line. It would also give huge bargaining-power to the Labour left.

And the SNP last night insisted it wanted to be part of any alliance. The party's Westminster leader, Angus Robertson, said: "From the outset of these negotiations, the SNP has made it clear that we believe a progressive alliance can deliver the best result for the people of Scotland – rather than a Tory government which was resoundingly rejected by the people of Scotland last week. We welcome the news that Labour and the Liberal Democrats are now moving towards this. The SNP stands ready to work with other parties in an arrangement which will deliver a functioning parliament at Westminster."