By Nick Assinder BBC News Online political correspondent

There are some animals that should never be allowed into your home.

They may look cuddly, eager and tame, but the minute you let them over the threshold they might tear up the furniture or scare the children.

And as far as many in the Labour Party are concerned, Ken Livingstone is just such a political animal.

If John Prescott, Gordon Brown and Charles Clarke - to name just a few - had their way, he would have been put down years ago.

You can take the beast out of the jungle but not the jungle out of the beast, they would probably say. But not Tony Blair.

Loyalty test

He has put his hand on his heart and admitted he was wrong about Ken.

Instead of being the "disaster for London" he predicted four years ago, Mr Livingstone has done a pretty good job for the capital.

According to the prime minister, on issues like crime, business and transport, he has been a success, and a moderate.

"I should be big enough to say the prediction I made four years ago has not turned out to be right," he said.

So, for the sake of party unity and the good of London, the anti-Ken brigade is just going to have to go along with the prime minister and put up with having him back in the fold.

What they fear, however, is that despite all the loyalty tests, it is only a matter of time before Mr Livingstone says or, more importantly, does something in direct defiance of the party leadership.

Hammer and sickle

The prime minister is clearly ready to put up with verbal outbursts from Mr Livingstone.

Asked about the mayor's recent claim that President Bush was "the greatest threat to life on this planet that we've most probably seen", he has shrugged his shoulders.

Ms Gavron could come fourth

It was not an offence to express views directly opposed to his own, he insisted.

But what if Mr Livingstone does something he should not?

One thing appears certain - short of murder or storming into Downing Street waving a hammer and sickle flag, there is no way he can be thrown out of the party again.

So to a very large extent, comeback Ken is now untouchable.

Londoners, meanwhile, appear ready, according to the polls, to give him another term in office.

Stitch up

And that, the critics claim, is the real reason the prime minister wants him back.

He can't stomach the prospect of seeing his previous candidate Nicky Gavron humiliated into fourth place in the mayoral election.

What Labour needs more than anything at the moment is a winner.

Meanwhile, the opposition parties hope that London voters will see this government about face for the cynical stitch up they believe it to be and actually turn against Mr Livingstone.

They believe many voted for him last time precisely because he was not a Labour candidate.

There would be a bitter irony if, after all the twisting and turning, Labour lost the mayoral election.

Don't put any money on it.