Currently, the only coronavirus vaccine available in the UK is the Pfizer/BioNTech vaccine that has been in use since early December, but ministers have set the wheels in motion to get the next vaccine out to two million people over the next two weeks, the newspaper reports.
Developed at Oxford, but licensed to AstraZeneca, the second vaccine is expected to be given the green light by medical regulators over the next few days, before it will be allowed out into the community.
The boss of the company behind the Oxford vaccine reckons the jab could be more effective than they first thought, too.
That would certainly be a piece of good news, with cases on the rise across the UK once again and a new variant - thought to be as much as 70 percent more infectious - causing havoc across London and the South East.
AstraZeneca boss Pascal Soriot told The Sunday Times that he thinks the researchers have discovered the 'winning formula' for their two-dose vaccine and promised they'd get all of the results from their tests out soon, in order to have the vaccine approved as promptly as possible.
Chancellor of the Exchequer Rishi Sunak praised the efforts of the vaccination staff on the NHS, as well as those who have developed them.
Speaking to the Mail on Sunday, he said: "There will be tough days and months ahead, but there are reasons to look ahead to a brighter future and what 2021 promises.
"The early roll-out of vaccines - and the incredible work of our scientists and NHS - means we can now see light at the end of the tunnel with this pandemic."
However, not everyone has been so impressed.
Some medical unions and the Labour Party have expressed their disappointment at the government's programme, arguing that they've not made nearly enough progress within care homes.
Nadra Ahmed, the chairman of the National Care Association, admitted the programme has been 'difficult', but added: "It's another case of the massive over-promise on something that just cannot be delivered. It's constant."
Shadow Health Secretary Jonathan Ashworth accused the government of making 'the same mistakes again' and being 'too slow' to get the vaccine into care homes on a wider scale.
So far, more than 600,000 people have had the vaccine, but the government expects to scale that up to around one million people each week in the new year.
The vaccine has only managed to be administered in care homes in seven areas.
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