Mikhail Khodorkovsky spoke out as Whitehall pursues lucrative new oil and gas contracts.
William Hague, the Foreign Secretary, makes his first official visit to Russia as Foreign Secretary next month.
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There have been signals from both sides that the countries are ready to patch up a relationship derailed by the murder in 2006 of Alexander Litvinenko, a critic of the Kremlin, in London.
Russia wants Britain to bring back preferential visa arrangements for its officials and to resume co-operation between the countries’ security services.
It also wants the authorities to extradite some of the many Russians who have made London their home after falling out with the Kremlin.
Britain is keen to compete on a level playing field with nations such as Germany when it comes to winning new business for its companies.
In particular, the Government is interested in British companies bidding for oil and gas contracts.
But Mr Khodorkovsky, who is regarded as a political prisoner by many in the West, urged caution. “Britain should not allow itself to forget that Russia remains an authoritarian state with an extremely high level of corruption,” he wrote in a Sunday newspaper.
“The export of this corruption to Europe is already visible, and presents no little danger to the UK.”
Mr Hague has said he wants a reciprocal improvement in British-Russian relations.
However, one stumbling block is the British demand for the extradition of the man accused of murdering Mr Litvinenko.
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