David Cameron has signalled Britain's readiness to rebuild a political relationship with Moscow despite a public vow by President Dimitri Medvedev that Russia would never extradite the key suspect in the Alexander Litvinenko murder case.

The Prime Minister, who arrived in Moscow yesterday, is the first British leader to visit Russia since the death of Litvinenko in 2006. After five years of political impasse British officials hope that by prioritising economic ties - including pushing Russia's membership of the World Trade Organisation - political and legal reform will follow.

"This is very much a long-term game," said one person on Cameron's delegation.

Speaking after the meetings, Foreign Secretary William Hague said there had been a patient, steady improvement in British-Russian ties as a result of the visit. He believed Britain now had a "working relationship at the very top of government".

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At a joint press conference with Medvedev in the Kremlin, Cameron hinted for the first time that the deportation of the former KGB agent Andrei Lugovoi need no longer be an impediment to closer ties.

"We can't pretend [difficulties] don't exist - we must continue to have frank discussions about them. At the same time it is right to rebuild an effective relationship on those things which are vital to the wellbeing of people in Russia and Britain."

Cameron ruled out reopening contacts between the British and Russian security services, though he said co-operation between the Serious and Organised Crime Agency and Russian police could be extended.

Medvedev held out no prospect of Russia ever extraditing Lugovoi to Britain and gave a tough response to British criticisms about corruption in the Russian legal system. "We all have to learn to reflect our legal frameworks," he said.

"I would like to remind you that Article 65 of the Russian constitution directly says that a Russian citizen cannot be extradited to a foreign state. That will never happen - no matter what the circumstances ... This is not possible. Please remember this."

Asked about corruption, he added: "Corruption exists everywhere. I open the secret to you that it exists in Great Britain as well but we are prepared to co-operate and invest in the UK."

Differences also emerged over Syria, where Britain is pushing Russia to agree to tough sanctions against the Assad regime. However, Medvedev offered little hope of an early resolution and expressed anger that Nato had over-stepped the meaning of resolution 1973 on intervention in Libya.

"We believe you should adopt a resolution which is tough and balanced," said Medvedev. "But it should not lead to the automatic imposition of sanctions.

"What is important for me is any resolution on Syria will not turn into resolution 1973 [on Libya]. Not in a sense of its content but in terms of its implementation in practice."

But despite some tough rhetoric British officials were pleased by the rapport between the two men during the one-to-one talks and will hope that it is Medvedev, rather than Prime Minister Vladimir Putin, who becomes the agreed candidate for presidential elections due to take place next year.

Hague said Cameron had an "excellent working relationship" with Medvedev. In contrast he said the Prime Minister had had a "businesslike meeting" with Putin.

Asked which areas the two countries could work together on, Cameron, who had just watched officials sign more than £200 million ($385 million) of trade deals, said: "We are mature and sensible countries and we should try to build a relationship which is in our interests."

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