Everyone aged over 25 in England will be able to book a vaccine from Tuesday, UK health secretary Matt Hancock has said.
Meanwhile Wales has announced it will complete vaccination six weeks ahead of schedule, with all over 18s to be given an appointment by next Monday.
The rollout in Wales has sped ahead of other UK nations, with 86 per cent of adults having been given a first dose, compared to 76 per cent in Scotland.
Some health boards in Scotland have opened vaccination to all over 18s, and in some island areas this group is nearly complete.
But nationwide there are still people in their 40s and 50s yet to receive a jag, while just over half of those aged 30 to 39 have been given one.
The Liberal Democrats called for Scotland’s rollout to be accelerated with walk-in vaccination centres in Edinburgh, where the rate of vaccination per population is lowest in the country.
Health spokesperson Alex Cole-Hamilton said: "For months I have pressed the Scottish Government about how NHS Lothian can be supported to speed up jabs. This week we finally saw military personnel deployed but these are few in number and are arriving late in the day.
"In areas like Bolton and Darwen, the government set up walk in vaccination centres to support those who had missed vaccine invite letters and make it easy for young people to get vaccinated in areas where caseloads were high.
He added: "Meanwhile the Welsh Government say that all over 18s will have had a vaccine invite by next Monday. There are clearly lessons that can be learned from what they have done. Thousands of my constituents are desperate to get vaccinated. They just haven't been given the opportunity."
Announcing the move to finish vaccination six weeks ahead of schedule, Mark Drakeford said on Monday: “I am very proud to say that Wales has one of the best Covid vaccination programmes in the world.”
The Scottish Government did not respond to a request for comment.