Brainwaves are unusual in the governance of men and it is rare that a knotty political problem invites a simple solution nobody had thought of before. But a conversation last week with The Spectator's newly appointed bullfighting correspondent (Lord Garel-Jones deplores the term but there is no other) has led us to a Eureka! moment. If anyone can see a flaw let him declare it, but his lordship and I are confident.
The dilemma we can crack runs as follows. Tony Blair is Prime Minister. Gordon Brown wants to be Prime Minister. Mr Brown is under the impression that Mr Blair has promised to make way for him, and Mr Blair has never quite denied the existence of some sort of understanding. Mr Blair is enjoying being Prime Minister and is in no hurry to stop. Mr Brown, who is not enjoying being Chancellor, is in a hurry to start.
The Parliamentary Labour party dislikes Mr Blair. A majority of them probably prefer Mr Brown. The Parliamentary Conservative party secretly admires Mr Blair. They see Mr Brown as a more suitable traditional socialist enemy.
The country, meanwhile, is in no mood to terminate Mr Blair's governance. Voters, including those who might be natural Tories, do not see the leader of the Conservative party as a convincing potential prime minister. Where Mr Blair does irritate voters is in his reformist rhetoric, unmatched by radicalism in action. He is timid at home and bold abroad, but his pretence to being some kind of a third-way saviour, when by his actions he reveals himself as a cautious temporiser, gets up the noses of reformers and conservatives alike. Many voters do not mind having a cautious temporiser as prime minister, but they do wish he'd stop promising to remake mankind. They contrast him with a chancellor whose instincts are straightforward, but in truth they are relieved that the Prime Minister is there to curb those instincts.
Two men, then: one happy in his job, the other promised (he believes) a crack at it. Our solution grants both wishes. It allows both Mr Blair and Mr Brown to be Prime Minister, though not quite at the same time. It allows Mr Blair to pay Mr Brown a debt of honour, yet does not deprive Mr Blair (not yet 50 and approaching the peak of his powers) of the chance to continue for as long as he and the electorate wish.
It is breathtakingly simple. Tony Blair should lead the Conservatives.
'Easier said than done,' you cry? On the contrary, easier done than said. The proposal sounds impossible, but examine it step by step, and you will see how it could work.
In a Personal Statement to the House Blair announces that he finds it practically, constitutionally and morally unsatisfactory to govern more with the support of the opposition than with that of the governing party. He has found it (he explains) agonising to organise war knowing that this is right but also that the party he leads does not support him. He has fought the firemen's strike more confident that the Tories understand why than that Labour do. In Cabinet he has wrestled a chancellor intent on expensive redistribution. He is tired of covering his back against sniping from Cabinet colleagues and restive backbenchers in his own party.
He has never, in short, been more confident of his programme for government or of his own unchanged political philosophy - essentially one of moderation - but is daily less confident that he can gain and hold the support he needs from the party he leads. Vulgar arithmetic may tell him that he can always win key Commons votes with Tory support, but his heart tells him that this is not right.
Finally (in a passage which intrigues commentators), he explains that his many years of opposition to the Tories have not been feigned; he feels there is much wrong with the party - some things, even, in the forces of conservatism which he hates. The party has struck him as sick in its spirit; but there are good men and women within it, good ideas and beliefs, too, and millions of good people in the country outside who want it to reflect their hopes and needs. It is failing them. The elements are there for a recovery. He wants to be involved. He is resigning, of course, as prime minister and will see the Queen later that day. He has done no deal with the Tories and joins them as a humble backbencher again.
Huge and spontaneous cheers from the Tories greet this speech, and as Mr Blair crosses the floor, hands reach out to grab his. They always knew he was one of them. On the government front bench, Gordon Brown smiles a little twisted smile.
His pleasure is short-lived. He is elected leader of the Labour party, naturally, for this has taken his potential rivals by surprise. Within days he is Prime Minister. Within weeks he is in trouble. The economy is sinking, public services are failing and the voters distrust him now that he's unleashed from Tony Blair. In foreign affairs Prime Minister Brown shows an uncertain touch. When the economy founders, he can hardly blame the last chancellor.
Within a year the polls are clear that Gordon Brown will struggle to be re-elected in 2005/6. A steady trickle of Blairite modernisers follow Peter Mandelson's lead and cross the floor to rejoin their former leader.
Tony Blair, obviously, assumes the leadership of the Conservative party. People begin talking about the possibility almost before the cheers greeting his switch die away. When he, Kenneth Clarke and Michael Portillo agree at a private dinner that he will lead an informal triumvirate, with Clarke his putative chancellor and Portillo at the Foreign Office, Iain Duncan Smith does the dignified thing and steps quietly aside. In the tremendous upswell of popular and media interest in this potential Government of All the Talents, even David Davis's ambition falters, and, fearful of losing support in his already marginal seat by standing against a Blair leadership, he backs down. John Redwood decides to give Blair a fight, but is trounced in the parliamentary election and (despite a decent showing) beaten in the run-off with Blair when the national Tory membership vote.
In May 2006 (Prime Minister Brown hangs on to the last as the polls slump) the general election victor, Anthony Charles Lynton Blair, leader of the Conservative party, is asked by the Queen to form a government. When he crossed the floor he took with him not only some of his own parliamentary party, but also millions of the voters he had recruited to New Labour. The Tories have an unassailable majority.
Don't laugh, because you never know. He might do it.
Matthew Parris is a political columnist of the Times.