Robert Dudley will be running TNK-BP from outside Russia
The British embassy in Moscow has warned of the damage being done by the dispute between TNK-BP's shareholders.
The oil company is half-owned by BP, with the other half owned by a group of Russian billionaires known as AAR.
The embassy said that their spat was damaging the economies of both Britain and Russia as well as harming the global energy market.
It also accused AAR's members of using parts of the Russian government to help them in their fight with BP.
"The way shareholders have manipulated elements of the Russian state bureaucracy and the way this has been allowed to continue is very disappointing," an embassy spokesman said.
"We will continue to stress to the Russian government the importance of a resolution between the shareholders in full accordance with the rule of law."
The Russian shareholders deny they want control of TNK-BP.
They insist their only goal is to remove Robert Dudley as chief executive of TNK-BP because they say he's not running the company in the interests of all those involved.
On Thursday Mr Dudley, said he was temporarily leaving Russia because of "sustained harassment".
This year TNK-BP has faced lawsuits, visa rows and industrial spying claims, as well as arguments about investment and the future role of Mr Dudley.
BP has withdrawn 150 of its foreign specialists from the country.
The Russian shareholders said the claims of harassment were "insulting", but still want Mr Dudley replaced because they claim that he is only running the joint venture in the interests of BP.
Bill Browder is currently fighting his own legal case.
Another businessman who has had problems doing business in Russia is Bill Browder from Hermitage Capital.
He was barred from the country three years ago, having become the biggest foreign investor in Russia.
He told the BBC that the high asset prices in Russia combined with the sort of problems BP is having makes Russia a bad place to invest at the moment.
"At this point you have no rule of law, no property rights and the prices are high - that's kind of a sucker's bet," he said.
The dispute between AAR and BP was one of the reasons for the fall in share prices on the Moscow Stock Exchange.
The benchmark Micex exchange had fallen 5% by mid-afternoon.
Many investors are concerned about the effect that the TNK-BP dispute will have on potential foreign joint ventures.
Sentiment was also hit by recent falls in the price of oil, with energy being such a big part of the Russian economy.
"The last train carrying the optimists out of Russian equities has just left the station," said Chris Weafer, chief strategist at UralSib.
"Let's hope it's just for a vacation rather than emigration."