The UK Government has offered to step in and help vaccinate Scots against coronavirus – as Nicola Sturgeon again faced claims that the programme is “lagging way behind” other parts of Britain.

Scottish Secretary Alister Jack has now written to the First Minister to “restate the UK Government’s full support in rolling out the vaccination programme and fighting the pandemic across the whole country”.

Of the 4.4 million adults in Scotland to be vaccinated, so far 610,778 have received the first jab – although Ms Sturgeon accepted that her government did want to “accelerate the overall progress” of the campaign.

She reported to MSPs that just under 35,000 first doses were administered on Monday – the highest daily total so far, and 55% more than the number of injections given on the same day last week.

But Scottish Conservative Holyrood leader Ruth Davidson noted that on Sunday January 31, “Scotland saw the lowest number of jags administered since the start of the mass rollout over a month ago”.

She hit out at the First Minister and said: “At the moment, all the evidence shows the Scottish Government’s rollout is slow, stuttering and lagging way behind the rest of the UK.”

While just over a fifth (21%) of 75-79-year-olds in Scotland have been vaccinated, Ms Davidson said that was “just a quarter of the proportion vaccinated south of the border” for the same age group.

Her challenge came as Mr Jack wrote to the First Minister offering the assistance of the UK Government.

He said: “I’m sure you would agree with me that it is in everyone’s interests that progress in vaccinating the people of Scotland matches the best efforts of the rest of the UK.

“With that in mind, we stand ready to offer any support or assistance we can give you to accelerate your rollout programme.”

The UK Government urged Ms Sturgeon to accept assistance, saying: “I strongly believe that to put the nightmare of Covid-19 behind us as quickly as possible, we must collaborate as closely as possible.”

Ms Sturgeon insisted that going forward the number of injections given will increase “as we make more use of mass vaccination centres for the younger age groups”.

Two new mass vaccination centres opened in Scotland on Monday, in Edinburgh and Aberdeen.

Meanwhile, 98% of older people living in care homes and 88% of staff working in them have been given their first dose of the vaccine.

“That really matters in terms of reducing the burden of illness and deaths,” Ms Sturgeon said.

She added that close to 90% of over-80s had now had their first vaccination, adding: “We will see the number in the over-70s group grow day by day in this week.”

All those aged over 70, as well as adults regarded as being clinically extremely vulnerable to the virus, would receive an appointment letter by the end of this week, Ms Sturgeon said.

She stressed: “More importantly, we are on track to meet the target we set to have vaccinated everybody in these groups with the first does of the vaccine by the middle of February.”

The First Minister said: “I’m not standing here denying we want to accelerate the overall progress.

“But nor will I apologise for having deliberately focused on maximising uptake in the most clinically vulnerable groups.”