Senior Conservatives are questioning whether Boris Johnson will need a national unity government or emergency cross-party council to share responsibility for the coronavirus crisis if the situation worsens.

George Freeman, a former minister in Johnson’s government, was the first to break cover to say a “Covid coalition” government may be “unavoidable” and some other Tory MPs privately believe the prime minister will need cross-party governing consensus if emergency measures are to continue for months.

Freeman told the Guardian: “The scale of this national emergency – the suspension of usual freedoms and democracy, the economic consequences and the likely loss of tens of thousands of lives – demands a suspension of politics as usual.

“When Labour have a sensible new leader, Keir Starmer [if elected] should be invited to Covid cabinet, Cobra and joint No 10 briefings.”

One argument circulating among some Tories is that Johnson may need to to share responsibility for decision-making with Labour and other opposition parties in order to survive the crisis, but he would need to convince the opposition that they would have meaningful input in return. One Tory MP said there was a political argument that Johnson may be keen to “drag Labour in” so the public do not associate the crisis solely with the Conservatives, if the situation worsens.

They fear that Johnson could end up losing public support – despite surveys currently showing he is strongly backed – if it looks like he alone is responsible for a crisis that ends up involving tens of thousands of deaths.

Johnson’s hero Winston Churchill ran a national unity government with Labour’s Clement Attlee as his deputy and Arthur Greenwood as a senior minister.

But one Tory MP said they already fear that even if Johnson comes to be regarded favourably like a Churchill, then the public could still be ready for a postwar Attlee-type figure – such as Starmer – if they want to see public services properly funded and rebuilt after the crisis is over.

Another Conservative MP said they thought No 10 would be considering a cross-party coronavirus council as an option if emergency measures have to go on for some time “as democratic consensus will be needed for a continued suspension of everyday life, especially if parliament cannot sit”.

Opposition politicians gave a mixed reaction to the idea of a national unity government. Starmer, the Labour leadership favourite, is focusing on trying to push No 10 to do the right thing on guaranteeing income and strict physical distancing, also called social distancing, rather than countenancing a national unity government.

However, Rebecca Long-Bailey, a rival leadership candidate is understood not to be ruling out the idea of more cross-party cooperation or even a government of national unity because of the crisis situation that the government finds itself in.

The third Labour leadership candidate, Lisa Nandy, said it would be better to draft opposition figures, unions, business groups and others on to a “national Cobra” than form an official unity government.

“Decisions are being made in real time,” she said. “Rather than having a reshuffle and trying to bed in a new government what you really need is a decision-making body that essentially takes this over until it’s dealt with.”

Labour would need to be among those represented, Nandy said. “There is absolutely no reason I can see why someone like Gordon Brown wouldn’t be in the meeting room, helping to steer us through this. He’s dealt with not just the global financial crash, but foot and mouth as well. We really do need to start drawing on a wider pool of expertise.”

A national Cobra would be better placed to spot issues with plans, Nandy said, and so avoid “what we’ve seen in the past few weeks, which is the government coming up with a plan, announcing it, the plan then unravels, and people are brought in to try and sort it out”.

A more cohesive approach was vital, she said: “My sense is people are losing confidence in what they are being told, and if people start ignoring advice we’re going to be in a new level of trouble”.

Layla Moran, a leading candidate for the Liberal Democrat leadership, agreed that rather than the disruption of rejigging ministerial posts in a formal unity government, a better approach would be “a more formal arrangement of cross-party working, through joint Cobra and subject-specific committee meetings”.

The government has engaged in some cross-party working so far, allowing Scotland’s first minister and SNP leader, Nicola Sturgeon, the Labour Welsh first minister, Mark Drakeford, and the DUP first minister of Northern Ireland, Arlene Foster, into emergency meetings.

It reluctantly allowed Sadiq Khan, the Labour mayor of London, into Cobra meetings in recent weeks. He revealed on Tuesday that there had been disagreement over whether construction sites should be shut, with the prime minister resisting such a move.