Boris Johnson on Sunday said the UK had vaccinated more than 15m people, as more than 60 Conservative MPs stepped up pressure on the government to lift the lockdown by the end of April.

The prime minister hailed the “significant milestone” as ministers signalled the NHS was “on course” to hit the target of offering inoculations to the 14.6m people most at risk from Covid-19 in the UK, including all over-70s and frontline healthcare workers, by the start of this week.

Johnson said he would on Monday outline in “full the details of the progress” made in the vaccination programme, but warned that the country still had “a long way to go”. Over the weekend, the government said that 90 per cent of over-70s had been given their first dose.

The NHS will on Monday begin vaccinating people aged between 65 and 69. Johnson said 1m letters had already been sent to that age group inviting them for their first jab.

Matt Hancock, health secretary, praised the work of the NHS teams alongside the armed forces, volunteers and local communities, adding: “There is so much more to do and I urge anyone eligible to step forward and take up their appointment. The vaccine is our route to freedom — we will beat this virus jab by jab.”

The announcement came after more than 60 of the governing party’s backbench MPs wrote to the prime minister over the weekend demanding a “road-map” for lifting all restrictions.

The letter from the Covid Recovery Group argued that if all nine priority groups were vaccinated as planned by the end of April, there would be no “justification for legislative restrictions to remain”. About 32m people fall within the nine groups, representing 99 per cent of deaths and about 80 per cent of hospitalisations from Covid-19 in the UK.

The CRG urged Johnson as a “national priority” to reopen all schools to all pupils by March 8 and also called for the reopening of pubs, restaurants and other hospitality venues by Easter, which falls on the first weekend of April, and for all other restrictions to go by the end of the month.

Ministers have in recent days reiterated their commitment to start reopening schools from March 8, with the government considering whether to open all schools in early March or opt for a phased approach with primaries returning first.

The backbench MPs said that after March 8, the burden would be on ministers to illustrate the “effectiveness and proportionality with a cost-benefit analysis for each restriction”.

Dominic Raab, foreign secretary, had said earlier on Sunday that while the government “shared the ambition” to lift lockdown measures, any lifting of coronavirus measures would be “evidence-led”, rather than relying on what he described as “arbitrary” targets.

“We are not making what feels to me like a slightly arbitrary commitment without reviewing the impact that measures have had on the transmission and the hospital admissions of the virus,” he told Sky News.

Raab also argued that the government needed to be able to “retain some flexibility” on the specific timetable of lifting restrictions in order to take into account the impact of numerous variants of the virus.

“We do need to be very careful how we proceed. We have made good progress. We don't want to see that unravel because we go too far too quick”, he said.

From Monday, UK residents returning from 33 high-risk “red-list” countries must quarantine in a hotel for 10-days on arrival.

The prime minister is set to give details later this month on how he plans to lift the lockdown in England, with the data on the impact of vaccines on coronavirus transmission due to be assessed by ministers in the coming week.