Jeremy Corbyn’s shadow cabinet deserve to retain their positions, an influential backbencher has said, as he urged MPs who have previously been critical of the Labour leader to back the party’s top team.

Clive Efford, the chair of the Tribune Group, which numbered more than 75 MPs before the election, praised the shadow cabinet for sticking by the Labour leader throughout the general election campaign, after which the party outperformed expectations.

There had been mounting speculation that the Labour leader, buoyed by 30 Labour gains and Theresa May’s struggles to form a government, could strengthen his team with experienced former ministers. Several Labour MPs, including Yvette Cooper, Angela Eagle and Chuka Umunna, have said they would serve in the shadow cabinet despite past criticism of Corbyn’s leadership.

Efford told the Guardian: “Jeremy has got a shadow cabinet that remained loyal and allowed him to perform extremely well during the general election. He can’t sack those people. They deserve to be rewarded for what they have done. We need to get behind those people and give them all the support [we] can.”

On Tuesday morning the shadow cabinet is due to hold its first meeting since the election last Thursday. Some shadow ministers, including the shadow home secretary, Diane Abbott, were criticised for their performances during the campaign.

Tribune relaunched in April with a new mission statement that was seen as a programme to win back traditional supporters while appealing to the centre ground. Those who signed up to the document included Cooper and the failed challenger to Corbyn in last year’s leadership contest, Owen Smith.

Efford said backbench MPs who once questioned whether Corbyn, the MP for Islington North, could gain support among traditional voters had been won over by his performance. “We questioned whether voters would be prepared to get behind Jeremy at a general election. The opinion polls suggested we were right about that. But it has to be said that Jeremy is a brilliant campaigner and did extraordinarily well. People have had a good look at him and found that they can get behind him. They see him as a credible leader.”

Efford said he would support any moves by Corbyn to reach out to new members if roles in his team became free. “I would like to see some new faces,” he added.

On Sunday, Corbyn said he was prepared to make overtures to MPs who had been critical of his leadership, hinting that he could broaden his shadow cabinet. But the shadow chancellor, John McDonnell, appeared more resistant to changing personnel and inviting Corbyn’s former parliamentary critics back into the fold.

Shadow cabinet members are expected to demand clarification on Tuesday over Labour’s Brexit policy, particularly about whether the party would negotiate to remain in the single market. Apparently conflicting statements on membership have come from the shadow Brexit secretary, Sir Keir Starmer, and Corbyn.

Starmer told BBC Radio 4’s The World at One on Monday he would like to see a “different tone and approach” to talks with the EU, including not pre-emptively ruling out continued single market membership. “What David Davis said this morning is that it’s not that the government doesn’t want membership of the single market, it’s that they’ve been told that you can’t have that with freedom of movement. It seems to me that would be a good place to start discussions, start negotiations, rather than simply taking it off the table.”

Asked on Sunday whether he was clear that Brexit would mean an end to single market membership, Corbyn told BBC1’s Andrew Marr Show: “Absolutely.”

A senior Labour source said there was confusion over their position. “Given that the government is in a mess and there is a real possibility of another general election, there will be even more scrutiny of our policies, particularly over Brexit. We need to get a negotiating position sorted, and fast.”

Labour MPs continue to fret over Brexit because some, particularly in seats where Ukip did well in 2015, had told voters that the party would leave the single market. Others, particularly in metropolitan areas, had said they would continue to fight to remain.

Barry Gardiner, the shadow trade secretary, told BBC Radio 4’s Today programme: “What we’ve said is that we need those benefits, and whether they’re achieved through reformed membership of the single market and the customs union, or through a new, bespoke trading arrangement, is actually secondary to achieving the benefits.

“It’s an open question as to what we can get. What we criticised [Theresa May] for doing is taking membership of the single market off the table right from the beginning.”