Alexander Litvinenko’s final testament, released after his death on Thursday evening, is deeply moving. It is also political dynamite. He thanked the hospital that battled to save him. He thanked his friends and the British authorities and paid tribute to the country that had granted him citizenship a month before his death. And dramatically accusing President Putin of having no respect for life, liberty or any civilised value, he said the Russian leader may have succeeded in silencing one man, “but a howl of protest from around the world will reverberate in your ears for the rest of your life”.

His death could not have come at a more awkward time for Mr Putin, who was meeting European Union leaders at an annual summit in Finland. During a tense press conference, he attempted to play down the case, offering condolences to the family but accusing Mr Litvinenko’s associates of playing politics with his death. But although his hosts did not bring up the murder in the talks on Russia’s long-term relations with the EU, it has strengthened suspicions of Mr Putin’s authoritarian administration and added to the ugly list of political murders and harassment of opponents that has heightened EU concern over Russia.

Those who should be pressing Moscow hardest to explain its role in this squalid assassination are the British police. This must now be a murder investigation. The hospital discovery that Mr Litvinenko was probably killed with polonium 210, a radioactive isotope, points to a sophisticated plot and to assassins able to obtain a substance not readily available except to those with considerable backing. The suspicion must fall on the FSB, the successor agency to the KGB. It had motive, means and opportunity. In exile in London, Mr Litvinenko, himself a former FSB agent, taunted and mocked the present head of Russia’s spy agency as well as Mr Putin. Goaded into a vendetta against a traitor, they may well have reacted as Henry II’s knights did on imagining their King’s desire to be rid of Thomas à Becket.

Two other factors increase the suspicion. First, the Russian parliament recently voted specifically to allow the FSB to undertake assassination missions abroad fighting terrorism. In doing so, it widened the definition of terrorists to include those who gave moral support to Chechen rebels and others seeking to undermine the State. FSB operatives, freed from any constraint, may well have seen Mr Litvinenko in that category.

Secondly, the FSB, though politically accountable, has been given an almost free hand by the President, who grew up in that same culture. It had no need to seek permission from the top. It knew that Mr Putin needed to maintain plausible deniability of all its actions. At the same time, it could easily point — as it now has — to the murky world of Russian exiles, some of whom are unsavoury characters and who are widely believed to have had links with organised crime groups while enriching themselves in Russia.

That murky world aside, Mr Putin has been deeply embarrassed by the murder. His open quest to make Russia respected again around the world is not helped by accusations of running a gangster state. He must, therefore, offer British investigators full co-operation and total access to all those they might want to question. A refusal or even prevarication must be taken as evidence of complicity. Nor should Russia be given the impression that this is a small episode that will be forgotten in a few weeks. Any policy of trying to tough it out should be met with an even tougher response from Britain. Mr Litvinenkno was a citizen of this country. His murder is an affront to our laws, our democracy and our way of life.