British finance minister George Osborne ruled himself out of the running to succeed Conservative Prime Minister David Cameron on Monday, citing his fierce advocacy of staying in the European Union.

"It isn't in my nature to do things by half-measure, and I fought the referendum campaign with everything I've got. I believed in this cause and fought hard for it," Osborne wrote in the Times newspaper.

"So it is clear that while I completely accept the result, I am not the person to provide the unity my party needs at this time."

Before the referendum campaign, Osborne had been widely regarded as a candidate to succeed Cameron one day, boosted by one of the strongest expansions among major developed economies in the last few years.

Osborne on Monday said Britain's vote to leave the EU was likely to lead to further volatility in financial markets but said the world's fifth-biggest economy would cope with the challenge ahead.

The Times said Osborne is weighing up whether to support former London mayor and Brexit campaigner Boris Johnson - the current front-runner - in exchange for an appointment as foreign secretary. It did not cite a source.

A YouGov poll on Monday suggested interior minister Theresa May holds a lead over Johnson, among both the public and Conservative party members.

British media also reported pensions minister Stephen Crabb and health secretary Jeremy Hunt were considering running for leader.