Interior minister Theresa May has vowed to unite Britain as she launched her bid to succeed David Cameron as prime minister with a letter to The Times.

The Conservative leader resigned in the wake of Britain's vote to leave the European Union in the June 23 referendum that sent shockwaves through the continent and across the globe.

Like Mr Cameron, Ms May supported remaining in the bloc but played a low-key and conciliatory role in the campaign that has seen her tipped as a unifying figure.

"Following last week's referendum, our country needs strong, proven leadership to steer us through this period of economic and political uncertainty, and to negotiate the best possible terms as we leave the European Union," Ms May wrote.

Her leadership would launch a "radical programme of social reform" that would "make Britain a country that works for everyone", she wrote.

In a swipe at her main rival, the mop-haired former mayor of London and prominent "Leave" campaigner Boris Johnson — who projects an eccentric and amiable image — Ms May wrote that a leader who understood hardship was needed.

"Some need to be told that what the government does isn't a game, it's a serious business that has real consequences for people's lives," Ms May wrote.

Mr Cameron promoted the 59-year-old vicar's daughter to Home Secretary following his 2010 election victory and she kept the role after his 2015 re-election.

Known as a hardliner on immigration, Ms May's stern demeanour and wardrobe of sober suits have drawn comparisons with 1980s Prime Minister Margaret Thatcher.

Mr Cameron's successor is expected to take office in early September and will face the prospect of assuming negotiations with the EU on Britain's relationship with the bloc and a decision on whether to call an early election.

AFP