The NHS has increased the daily rate of booster vaccinations by three-quarters in a week – but remains short of the roughly 1.5m jabs a day needed to match Boris Johnson’s promise of a booster jab for all those eligible by the end of the year.

One group of health service bosses said the NHS “should not be blamed” if the target is not met, reflecting concern there could be political recriminations if the goal set by the prime minister just over a week ago is not reached.

On Monday, 897,979 boosters were administered around the UK, compared with 513,722 a week ago, the day after the prime minister brought forward the vaccination target in a televised address.

There remain 15.1 million people across the UK who had a second jab before the end of September and have not yet had a booster – and there are 10 days, excluding Christmas Day, to complete the programme in line with the prime minister’s pledge.

Johnson had promised that everybody eligible aged 18 or over “will have the chance to get their booster before the new year” – a commitment that applied to England but has been matched by Northern Ireland. Wales has pledged to offer the jab to all able to receive one by the end of the year.

NHS bosses were not given any notice of Johnson’s commitment. Saffron Cordery, the deputy chief executive of NHS Providers, which represents NHS Trusts, said it had always known the pledge was ambitious – and emphasised the speed at which the number of vaccinations had been increased.

“We must avoid a situation where blame is placed on the NHS, when staff are working completely flat out to get jabs in arms at a time when they are also working through a significant backlog of routine care,” she added.

Scotland, however, has already walked away from matching Johnson’s promise. Nicola Sturgeon, the first minister, wants 80% of the eligible population vaccinated with boosters before the new year and, on Tuesday, said she was confident that target would be met.

The figures for England show that 753,793 people received a booster on Monday, leaving 12.5 million people who have had a second jab still awaiting the extra vaccination. That amounts to more than 1.2m jabs a day over the remaining 10 days. Adding Northern Ireland and Wales leaves 13.8 million eligible people to go, a required rate of 1.4m a day.

Labour’s health spokesperson, Wes Streeting, said the party had called on ministers to increase the booster programme to half a million a day in October. “The government’s delay has left the NHS with a difficult target to hit, but if anyone can do it, they can.”

But the Conservatives said the party would not take lessons from Labour. “They wanted to keep us in the European Medicines Agency – if we had listened to them our world-leading rollout would have been massively delayed,” a party source said.