Boris Johnson will probably succeed when it comes to selling his new three-tier system of coronavirus restrictions in England to the public, but persuading fractious, lockdown-sceptic Conservative MPs to buy it will prove more tricky.

The public will understandably be most interested in the temporary relaxation of the rules allowing them to meet family and friends over Christmas. It seems that three households will be able to gather over a five-day period. Details are expected tomorrow after ministers hold further talks to secure UK-wide agreement with the devolved administrations in Scotland, Wales and Northern Ireland.

Some people living in the highest-risk, tier 3 areas will be less happy to learn that their pubs will remain closed and restaurants will be limited to takeaways. However, opinion polls suggest that, despite evidence of “Covid fatigue”, most people broadly support a “public health first” approach.

That cannot be said for Tory MPs. Some 70 signed a letter to Johnson at the weekend warning that they might not support the tougher local and regional measures that will replace the lockdown in England ending on 2 December.  They say that the cure risks being worse than the disease because of the harm to mental health, poverty, livelihoods and the economy.

The MPs, part of the recently formed “economy first” Coronavirus Recovery Group, have demanded a full cost-benefit analysis of the new proposals, saying: “The burden is on the government to demonstrate the necessity and proportionality of each restriction.” Ministers are unlikely to publish such an analysis, saying that it is difficult to predict the precise outcome of the curbs.

The Coronavirus Recovery Group will welcome the decision that all shops in England will be able to open again — crucially, in time for the Christmas trade. But it will be worried about the more-severe-than-expected impact on pubs and restaurants under the system that Johnson is announcing in the Commons today before areas learn on Thursday which tier they will be in.

Iain Duncan Smith, the former Tory leader, dismissed the new regime as “in effect, a national lockdown by another name”. That’s not strictly true, as shops, hairdressers and gyms will reopen, but it shows the strength of feeling among Tories who think the current lockdown unnecessary because the previous tiered approach was working. Nus Ghani, a former transport minister who supported the current shutdown, said: “We cannot continue to live in this childlike fashion, under repeated cycles of damaging lockdowns and apparently arbitrary restrictions.”

Although they might not say it in public, many Tory MPs will agree with Andy Burnham, the Labour mayor of Greater Manchester, who told Radio 4’s Today programme that closing hospitality in tier 3 areas would be “devastating” for the sector and for cities in the north.

He said the government “seems to be going too far before Christmas to allow too much over Christmas and that will lead to a huge loss of hospitality businesses, which I would say is too big a price to pay”. A reminder to Johnson that it is impossible to please everyone.

The Tory awkward squad do accept that ministers are listening to their concerns. As evidence of the “exit strategy” they are demanding, they will welcome the extension of mass testing so that close contacts of people who test positive no longer need to self-isolate for 14 days. The good news about three vaccines, including today’s breakthrough by Oxford University, will improve Tory morale.  However, voting for the new blueprint in the Commons will still be a stretch for many Tory MPs. Fifty refused to support the government when the current lockdown was imposed, in theory enough to overturn Johnson’s majority of 80.