It's already happening. There are now more than 40 joint administrations at local government level in England - local authorities where the two parties have shared out committee chairs and work co-operatively. But the best example of co-operation has been in Scotland, with the development of a joint and agreed policy on a devolved Scottish parliament.
These discussions have been remarkable. Nothing like them has happened before in domestic politics. There is no reason why we can't have similar exchanges in other areas of policy between now and the next election. If these enjoy the same success, they could lead to discussion about actual legislation after the election.
With that in prospect, the near-hysterical response of some Lib Dems to Tony Blair's offer of co-operation beggars belief. The Lib Dems, after all, have preached open and plural politics for decades. And yet when a Labour leader, determined to break the mould of British politics, reaches out the hand of co-operation, the Lib Dems have responded with tribalism at its childish worst.
They have absurdly paraded the Liberals as the party of pure and unsullied principle. Indeed impotence is an easy road to virtue. Equally ludicrous have been the attacks on the Labour Party for changing and updating its policies. This from a party that had abandoned its hallowed and defining principle of "equidistance" only the previous evening.
Hopefully this attack of the vapours will pass and Lib Dems can knuckle down to the difficult business of preparing a practical agenda for government. Macho stances on taxation are no substitute for serious economic analysis. Parties contending for government have to make commitments they know they can deliver.
We should waste no more time on these mock-virile posturings. What is needed instead is patient and responsible work on what is possible and practical to deliver the change that Britain needs. That is what was achieved in the devolution discussions, and that model ought now to be applied to other areas of policy.
Co-operation simply means being honest with the electorate and with ourselves. The public is quite aware of the huge areas of overlap in many Labour and Lib Dem policies. Of course there are differences in detail, but what strikes most people is the extent of the common agenda shared by the two parties and how radically it differs from that of the Tories.
We need more than a change of government in Britain. We need a new politics. It is only by honest, sensible and reasonable co-operation that we will achieve it.
The writer is Labour MP for the Western Isles.