Treasury officials have been assigned to work on the government's “road map” for lifting England’s coronavirus lockdown, to ensure that scientific information is matched by rigorous economic advice.

Boris Johnson will set out his plan for coming out of England’s lockdown in the week beginning February 22, and the prime minister is expected to publish proposals for a phased reopening of the economy.

Schools could reopen from March 8, but no decisions have been made on the plan for the rest of the economy.

Some ministers expect that non-essential shops may not reopen until April, followed by the hospitality industry in May. This would anger backbench Conservative MPs who want the economy fully restarted as quickly as possible.

Last year tensions opened up between Mr Sunak and Mr Johnson over the pace of the economy’s reopening after England’s first lockdown.

Mr Sunak, who pushed for a swift reopening, felt the government’s “cautious” scientific advisers wielded too much influence and urged Tory MPs to make the case to the prime minister for a faster easing of restrictions.

Government officials said that Mr Johnson and Mr Sunak were now meeting “almost every day” to discuss the plan and that the prime minister had asked Treasury economists to help draw up the road map, due to be published in the week starting February 22.

Mr Sunak wants to lift the lockdown as swiftly as possible, but his allies also said he supported a “cautious” approach that ensured that Covid-19 was brought fully under control.

The government looks to be on course to reach its target of vaccinating 15m Britons in the four most at-risk groups — elderly care-home residents, frontline NHS workers, the clinically vulnerable, and those aged over 70 — by February 15.

Once that milestone has been reached, the government will set out a timetable for offering first doses of a vaccine to 17m Britons in the next five priority groups.

Chris Whitty, England’s chief medical officer, said that while vaccinating the 15m most vulnerable Britons will reduce Covid-19 related deaths by 88 per cent, the pressure on hospitals will only be significantly reduced by giving jabs to the next 17m people. Any major easing of lockdown restrictions before that point is therefore unlikely.

Nadhim Zahawi, the vaccines minister, said the government was moving “as quickly as possible” to vaccinate all nine priority groups, and that the economy would reopen “gradually”.

He told the BBC that people could “do the maths” on when the nine groups would receive their first vaccine dose — which implied early April.

Mark Harper, chair of the lockdown-sceptic Covid Recovery Group of Tory MPs, called on the government to “get rid of restrictions completely” by the end of May, assuming vaccine supplies remain steady.

Tory MPs are keen for pubs and restaurants to restart by the time of local council elections, due on May 6, because Conservative campaigners are hoping their party will benefit from a successful vaccine rollout.

One minister admitted that once schools had reopened, “keeping locked down” would be difficult.

Mr Sunak has told colleagues he wants his Budget on March 3 to be the last time he has to extend state support measures for companies and households.

“He doesn't want there to be another lockdown,” said one Treasury official, a view shared by Mr Johnson.

The chancellor is expected to use the Budget to extend into the summer such measures as the furlough scheme and a business rates holiday for companies, possibly tapering off government support over a number of months.