But Mr. Fridman has a business track record that might be hard for the Cameron government to admire. During Mr. Browne’s reign at BP, he and Mr. Fridman set up a Russian joint venture called TNK-BP in 2003.

It was a partnership fraught with tension, with boardroom battles and struggles for control that at times found their way into international courtrooms.

But sometimes the disputes were settled in murkier ways, inside Russia. Analysts say there was little doubt that Mr. Fridman and other TNK partners had the support of Russian regulatory and law enforcement agencies. At one point after Mr. Browne had left BP, for example, men in masks and toting assault rifles turned up at BP’s corporate offices in Moscow. A Russian minority shareholder had sued the TNK-BP partnership, and the security forces showed up to serve a warrant. Whatever the legal basis, it looked like nothing less than typical and blunt Russian intimidation tactics on the part of Mr. Fridman and his partners.

Not until TNK-BP was sold to the Russian state-controlled energy company Rosneft in 2013 were the fights between TNK and BP finally put to rest. Mr. Fridman and his TNK partners reaped about $14 billion from the transaction.

”TNK shareholders pretend that they are not connected to the Kremlin, but how else can you explain the help they seemed to receive from the authorities,” said Ilya Zaslavsky, a former TNK-BP employee and independent energy consultant based in New York.

Apart from any sanctions that might be aimed at Mr. Fridman personally, if industrywide sanctions were imposed against the Russian energy industry, they could affect L1 Energy — though it is unclear how such sanctions might apply to assets owned by Russian nationals who are outside of Russia.

Though a shaky truce is in place in Ukraine, and the European Union on Monday was trying to broker a new deal between Gazprom, the Russian gas exporter, and Ukraine to keep gas flowing, pressure has been building to impose new sanctions for violations of the cease-fire in the days after it was signed on Feb. 12.