Britain must know that the chance of Russia handing over Andrei Lugovoy to face the charge of murdering Alexander Litvinenko is almost zero.

So if it presses hard on its extradition request, it will put relations into deep chill for some time. That may be exactly the kind of firm message which Tony Blair wants to send as he leaves Downing Street. If so, he has chosen the right moment; the fights that Russia has picked with its neighbours and with EU countries will give him plenty of support. All the same, the Government will have to think carefully about what it wants to get out of the dispute if, as seems all but certain, Russia will not extradite Lugovoy.

For Russia’s part, its reaction will show whether it is spoiling for a broader fight, or whether, if it isolates the issue, it wants to keep hold of common ground on other fronts. The first reaction from Moscow was unambiguous: Russia could not extradite Lugovoy to Britain because of a constitutional ban on handing over a Russian to another state, the Prosecutor-General’s office said. Russia’s criminal code also rules out extradition of a citizen for committing a crime abroad, a second legal line of defence.

However, Russian prosecutors left open the possibility that he could be tried in his homeland, a way of offering a compromise, should Russia want, although not one in which Britain might have much confidence. The Kremlin has dismissed as ridiculous Litvinenko’s deathbed accusation that President Putin commissioned his death in retaliation for his sustained criticism.

Britain’s dilemma does not lie with the Crown Prosecution Service. Sir Ken Macdonald, the Director of Public Prosecutions, rightly called the murder an “extraordinarily grave crime” in announcing that he regarded the evidence passed to him by the police as strong enough to bring charges.

He was understating its resonance, if anything; it was a grisly poisoning, leading to an enormously painful death, which polluted Central London, and swept a jangled country back in imagination to the dark plots of the Cold War. The capacity of polonium-210 to leave a forensic science trace across Europe, surely not intended by whoever devised the scheme, is the only good thing to be said about it.

Downing Street has kept very properly behind the independence of the judicial process, however sceptically the notion might be regarded by some in Russia. It would not comment on how it may respond if Russia turns down the extradition request. But that is too obvious a question to ignore.

It does not want to break political and economic ties with Russia, needing its help urgently on Iran, Kosovo, and climate change, for a start. But nor would it want to step back and appear to accept such a murder on its soil.

There is nothing in the case which is going to make relations between Britain and Russia warmer. The question is how much chillier they get, and how far they choose to let the row spread to other areas of common ground.

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