Britain and Russia have uniquely bad relations with each other - far worse than between Russia and any other main EU country, and worse than Russia's relations with the United States. This frostiness was highlighted again yesterday when a new spying row broke out after the Russians accused a senior diplomat in Moscow of working for British Intelligence.

So it is hardly surprising that the one-hour meeting this week between Gordon Brown and President Medvedev at the G8 summit in Japan failed to resolve five years of bickering between Britain and Russia.

It is reported that Mr Brown raised three issues: the murder of the KGB defector Alexander Litvinenko in London two years ago and Russia's refusal to extradite the British Government's prime suspect, Andrei Lugovoi, to face trial; the closure of British Council offices in Russia last year; and the continuing TNK-BP dispute. The history of such “issues” goes back to 2003, including asylum, visas and the harassment of Tony Brenton, the British Ambassador in Moscow by a Kremlin-inspired youth movement called Nashi.

Russia's decision to close all British Council offices outside Moscow was - in theory - based on a squabble over back taxes, but it was also part of the tit for tat that followed the Litvinenko murder. There is no reason why the British Council offices should not reopen by the end of the year.

Ironically, it illustrates a trait that the British and Russians share, which is relying on personal relations and informal procedures to get things done, without tying everything down in a tight contract. This works fine as long as overall relations between the two countries remain good. If anything sours them, both countries mount their high horses of legalism, the Russians more than the British.

The unravelling of informal understandings is also the underlying motif of the TNK-BP spat. The Russian consortium of oligarchs which owns the oil company TNK formed a 50-50 partnership with BP as an insurance against suffering the fate of Mikhail Khodorkovsky, the former Yukos boss, who lost both his company and his liberty in 2003 when he was found guilty of fraud. They no longer need BP for this purpose, instead they want it to spearhead the company's international expansion.

But BP wants to concentrate on exploiting oil reserves in Russia. So there has been a struggle for control of the company. Until recently Lord Browne of Madingley, the former chief executive of BP, would smooth over any friction by flying over for private chats with Vladimir Putin. With this informal channel removed, the Russian investors have reverted to the traditional tactic of getting the Russian State to hold up visa renewals for British TNK-BP executives, and start investigating violations of labour laws and tax evasion. It's all rather reprehensible, but, like Shell, which suffered from such attention earlier, BP went into Russia with open eyes in search of super-profits, and there is no call to involve the British Government on its behalf when the going gets tougher than expected.

There is a complete standstill over Litvinenko-Lugovoi. Britain missed a trick by not proposing a trial in Moscow on the condition that the Crown Prosecution Service would be free to give its evidence, which has never been made public, in open court. The Russians would probably have turned this down, but we would have gained kudos. Instead, we told the Russians to change their constitution, and started the useless tit-for-tat policy of expelling diplomats. It's now too late to retrieve the position, as Lugovoi's election to the Duma gives him immunity from prosecution.

It's plausible to believe that the Russian State ordered Litvinenko's murder, provided we are clear that the Russian State is not a monolith and that every order to kill does not have to be personally signed by the President. But what was a “senior official” of the MI5 doing telling the BBC that the Russian State killed Litvinenko, just before the Brown-Medvedev meeting? Military Intelligence is a branch of the British Government. Did the Government order the leak? Or was it private initiative by an MI5 officer? Problems of assigning responsibility for state actions are acute in the Russian system, but they are not absent in our own.

So where we do we go from here? The answer would be to put the Litvinenko affair into cold storage, and for the British Government to be much more cautious in granting asylum to people accused of serious crimes in Russia. These are simple steps but there are greater stumbling blocks to Anglo-Russian friendship.

One obstacle is the assiduously promoted view that Russia is slipping back into dictatorship, that we are on the brink of a new “cold war”. I don't think the British Government believes this, and would be wrong to do so. Commentators and politicians who talk of a regression under Mr Putin forget how horrible the 1990s were for most Russians. These quarrels are properly called “spats” between two important countries that have a great deal to gain from co-operation on much more important issues, ranging from nuclear proliferation to climate change.

Nevertheless, there is a gap in perception that may reflect both countries' imperial pasts. The Russians, struggling to come to terms with the loss of their own empire, are quick to accuse the British of imperialist designs on them. The British can't get over the feeling that it is their duty to lay down the law to lesser breeds. It is this mixture of Russian cussedness and British condescension that converts spats into more serious disputes.

But there is also something else. At some point the Blair-Putin relationship broke down. This is probably because Mr Blair was seen to be President Bush's vassal, and therefore Russia had no incentive to give any special consideration to British interests and wishes. Why talk to the monkey when you can talk to the organ grinder? Britain would get more respect from Russia if it was more independent from the United States. This is a lesson Mr Brown could usefully take away from his tête-à-tête with Medvedev.

Lord Skidelsky is a columnist for the Russian newspaper Vedomosti

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