Sir Keir Starmer’s approach to governing “doesn’t necessarily work in politics”, a cabinet minister has suggested.

Addressing the No 10 setup during her former boss’s premiership, Yvette Cooper suggested that new prime minister Andy Burnham is better equipped for “a world of social media”.

Sir Keir stepped down as prime minister last month, promising his “full support” to Mr Burnham.

Under Sir Keir’s tenure in Downing Street, Ms Cooper held posts in the cabinet as home secretary and subsequently foreign secretary.

She currently serves as health secretary within Mr Burnham’s cabinet.

In an appearance on the podcast with former chancellor George Osborne, Ms Cooper remarked that “it’s important to recognise” Sir Keir’s six years leading his party.

“That, in itself, is unusual now,” Ms Cooper said, adding she thought Labour faced an “existential crisis” when Jeremy Corbyn – now the independent MP for Islington North – led the party.

“I don’t think we’ve done government very well in the last couple of years,” she added.

“I think we’ve been pursuing a lot of really important things – a lot of things we’ve made massive progress on and achieved.

“We’ve got 3,000 more neighbourhood police on the beat in the first year, really big shift for somewhere like Castleford town centre.

“We’ve got NHS waiting times and lists coming down.

“You’ve got a whole set of things, you know, new policies being introduced that make a massive difference but I think the focus shifted quite a lot.

“So, we had ‘missions’ in the first six months and then they kind of disappeared.”

Ms Cooper also said Sir Keir had “a style of leading the Government that maybe doesn’t necessarily work in politics”, because he had a “bring me solutions, not problems” style of management.

Referring to immigration reforms which were launched during her time in the Home Office, she said: “It was like, ‘well, you can sit in the front row of the launch but actually, the prime minister’s going to launch it’.

“But actually, the prime minister’s not really been involved in the development of policies.”

Ms Cooper said that in “contrast”, the prime minister Andy Burnham’s drive to reform social care has largely “come from Andy because it’s something he’s been passionate about”.

The prime minister has pledged to work cross-party to create a care system where patients can “move seamlessly between hospitals, home care and community services”, while being “fully and sustainably funded”.

Ms Cooper continued: “He wanted to then talk a lot about – what are the problems here? How should we be thinking about it? How should we be trying to solve it?

“And he wanted me to be part of the event launching it, to be speaking at it, to be talking about it.

“And I think there’s, maybe there’s a difference in style of operating.”

Ms Cooper also said that “in a world of social media, it’s really obvious what he cares about, feels, can feel passionate about” while at the same time being “a lot older” than he was when he left parliament in 2017 to become the mayor of Greater Manchester for almost a decade.

The health secretary had earlier told the podcast she wanted to be the shadow health secretary when Labour was in opposition.

Referring to the reshuffle when Mr Burnham became prime minister, she said: “Twenty-seven years ago, I was a junior health minister.

“So, on the one hand, there’s this amazing, this incredible job and on the other it’s, ‘hang on, this is a massive shift’.

“You’re having to switch the things that you’re focused on and, you know, having had a series of different reshuffles, there’s obviously something frustrating about all of those things you were working on that you’re no longer able to see through, things that you wanted to do, and so on.”

But joining the Department of Health and Social Care presented an “amazing set of opportunities”, she added.