Jeremy Corbyn is expected to delay any reshuffle of Labour’s shadow cabinet to focus pressure on the Conservatives, though senior sources hinted those MPs who had stayed loyal to the Labour leader would not be removed in favour of more high-profile names.

Several Labour MPs, such as Yvette Cooper, Angela Eagle and Chuka Umunna, have said they would serve in the shadow cabinet despite past criticism of Corbyn’s leadership. Eagle said she would “play any part my party should ask of me” while Umunna said he would do so “if asked but I make absolutely no presumptions”.

A senior Labour source said the party’s shadow cabinet had been “stepped in, stepped up and done everyone really proud” during the general election after many MPs doubted their abilities and Corbyn’s leadership.

“Bringing people together doesn’t necessarily mean that the people who have been absolutely fantastic getting moved out of post,” the source said. “Jeremy’s approach has been vindicated and he has authority.”

On Sunday, Corbyn said he was prepared to reach out to MPs who had been critical of his leadership, hinting he could broaden his shadow cabinet. “I’m the most generous person in the world,” he told the BBC’s Andrew Marr Show. “I’m not going to appoint the shadow cabinet here on the programme. Yes, of course we are going to reach out, ever since I became leader I had reached out.

“There’s been one or two difficulties at times with the parliamentary party but let’s put that behind us. The party came together around a brilliant manifesto and came together for a result that you and many others never expected.”

The shadow chancellor, John McDonnell, appeared more resistant to changing personnel and inviting Corbyn’s former parliamentary critics back into the fold. “Our shadow cabinet at the moment was a winning team,” he told ITV’s Peston on Sunday, though he said he thought Labour’s top team should “draw upon all the talents” when the party reassembles next week.

“It just won effectively votes that no one predicted that we would so I don’t want to break up that winning team.”

McDonnell said it was ultimately “for Jeremy to decide” whether changes would be made to the shadow cabinet, but added: “There are a number of vacancies that’ll be coming up almost certainly, in addition to that there’s other roles people can play.”

However, another senior Labour source said it would become clear the pair did not have a difference of opinion. “John and Jeremy both agree on this,” the source said. “There is never more than a fag paper between them.

“There’s a lot of talent, we always want to include people and bring them on board and there are vacancies to fill but that’s up to Jeremy. And Jeremy is an exceptionally loyal individual.”

However, another source said the party wanted to concentrate its efforts on challenging the Conservatives and May’s authority as prime minister, rather than expending energy immediately on personnel changes. “It’s not the priority to be thinking about these things now,” the source said. “Her lack of authority, her lack of credibility, how she doesn’t have a mandate, that’s the priority.

“The second focus is preparing to serve in government and step up if that’s possible. The third focus is our plans around opposing the policies they want to push through. All those things take precedence.”

Who could join the shadow cabinet?

Yvette Cooper

The former shadow home secretary looked to be preparing for her own leadership bid had the election gone differently. Cooper has useful history with Corbyn and with May, leading his refugee taskforce and sparring with May while she was at the Home Office. The Labour MP’s barbs in the Commons seem to get under May’s skin.

Chuka Umunna

Another MP who may have been planning his own leadership bid, the Streatham MP has kept his own profile high as chair of Vote Leave Watch and a prominent advocate for a soft Brexit which chimes with the party’s young supporters. On the right of the party, appointing Umunna would be a conciliatory move, he was one of Corbyn’s most strident critics after the referendum last summer but has remained quiet on the leadership issue since then.

Dan Jarvis

The former paratrooper suggested he would interested in a frontbench job after the leadership election last summer. Although he is not on the party’s left, he is also not aligned with a particular faction so may be seen as a well-known face safe to bring on to the pitch.

David Lammy

The Tottenham MP won a huge majority and would be a good pick for a job at justice or communities. A former minister in the Blair government, Lammy has also been a prominent voice on both Brexit and Donald Trump’s presidency. However, bringing in yet another London MP when many of the rest of Corbyn’s top team already come from the capital may count against him.

Caroline Flint

McDonnell appeared with Flint on ITV on Sunday morning and praised her work on forcing multinationals to publicly declare where they do business and the tax they pay. The shadow chancellor called her “superb, amending legislation, drafting it up from the backbenches, working with us, it’s that sort of work and cooperation that we want to continue on”.