Openly gay MP Ben Bradshaw has been appointed as the new culture secretary, replacing Andy Burnham, who is to take over his role as health secretary.

The latest reshuffle means that there will be three openly gay figures in the cabinet, as Peter Mandelson is currently the business secretary and Nick Brown is the chief whip.

Mandelson has been offered enhanced responsibilities, taking on skills, innovation and science, along with the new title of first secretary of state. He has long wanted the position of foreign secretary, a role once held by his grandfather Herbert Morrison, but current foreign secretary David Miliband has kept his title.

Former BBC journalist Bradshaw will have only days to decide the fate of Channel 4, as the Digital Britain report is set to be published on June 16th. Other issues at hand include how the digital switchover licence fee surplus should be used, preserving regional news provision on ITV and handling plans for universal broadband.

He was caught up in the expenses scandal but accused the Daily Telegraph of being “homophobic” in the way it exposed his claims.

Announcing the reshuffle at a press conference today, Gordon Brown vowed to press ahead “further and faster” to “finish the work” he had begun as prime minister.

“If I didn’t think I was the right person leading the right team, I wouldn’t be standing here. No one could forgive a Labour government if we walked away from our duties … I have the determination to continue,” he said.

“I will not waiver, I will not walk away, I will finish the work.”

Minister for Europe Caroline Flint, who last week gave an interview to PinkNews.co.uk, resigned in the middle of the prime minister’s press conference. Glenys Kinnock is to be appointed in her stead.

Flint launched a scathing attack on Brown in her resignation letter, saying he had “strained every sinew” of her loyalty to the government.

She added that he had created a “two-tier government” in which women ministers were treated as “little more than female window dressing”.

Transport secretary Geoff Hoon and employment secretary Tony McNulty also resigned during Brown’s speech.

In other moves, universities secretary John Denham is to succeed Hazel Blears as communities secretary, while Yvette Cooper replaces James Purnell as work and pensions secretary. Liam Byrne will replace her as chief secretary to the treasury.

Bob Ainsworth is to replace John Hutton as defence secretary after Hutton quit earlier this week. Alan Johnson has replaced Jacqui Smith as home secretary.