Boris Johnson was on Monday urged by Conservative MPs to set a March 8 target for easing coronavirus restrictions after ministers insisted 15m of the most vulnerable people in the UK would be offered a vaccine by mid-February.

The Department of Health said 2.3m people had been vaccinated since early December, and health secretary Matt Hancock said he was “confident” the government’s goal of reaching 15m would be met by February 15.

However, Tory MPs sceptical about England’s lockdown seized on progress with vaccinating four priority groups of people — those over 70, health and social care workers and the clinically vulnerable — to demand a plan from the prime minister for lifting the restrictions.

Mark Harper, chair of the influential Covid Recovery Group of Conservative MPs that has raised questions about the restrictions, called for the government to set out “a route back to freedom” from the measures.

“If we hit the crucial February 15 deadline, the four top-risk groups will have immunity by March 8 — three weeks after the last jab,” he said.

“At that point — once all the key groups have become immune to Covid — what possible reason could there be for keeping severe restrictions in place a second longer?”

Mr Johnson expressed concern the public might develop “false complacency” about the need to comply with current restrictions because of progress with the vaccine programme, even though the NHS was under severe pressure.

“The worst thing now would be for us to allow success in rolling out the vaccine programme to breed any kind of complacency about the state of the pandemic,” he said.

According to the vaccine delivery plan for the UK published by the government, ministers are proposing to establish 2,700 sites for administering jabs.

These sites include 50 mass vaccination centres, seven of which opened for the first time on Monday, including one at Epsom racecourse in Surrey. About 206 vaccination hubs are due at hospitals, plus a further 1,200 local sites, many involving general practitioners or community pharmacies.

The government has enlisted a workforce of 80,000 professionals to run its vaccination campaign, and a further 200,000 people have volunteered to help.

In England, the government is aiming for all residents and staff in more than 10,000 care homes to be offered vaccine jabs by the end of January.

Ministers also want the vast majority of people in England to have access to a jab within 10 miles of their home.

To reach 15m people by mid-February, an average of 2.5m would have to be vaccinated every seven days for the next five weeks, although some may decline jabs.

Currently, about 200,000 vaccinations are taking place each day, equating to about 1.4m a week.

Mr Hancock admitted that supply of vaccines was slowing down the rollout, saying: “The supply of vaccine is the current rate-limiting step — we will bring forward as much vaccine as becomes available.”

Kate Bingham, former chair of the government’s vaccine task force, acknowledged that the main supply bottleneck in recent weeks had been manufacturers’ ability to scale up production. “We don’t have these manufacturing facilities at full scale,” she told MPs.

Meanwhile, chancellor Rishi Sunak told MPs that England’s third lockdown since last March would have “a further significant economic impact”, adding: “We should expect the economy to get worse before it gets better.”