GPs in the region have told The Yorkshire Post that not being able to get hold of enough of the Pfizer and AstraZeneca vaccines is the main limiting factor as they race against time to protect the vulnerable from Covid-19.
Boris Johnson said yesterday that 3.2 million first doses of the vaccines have already been administered around the UK including a quarter of a million in one day, far more than anywhere else in Europe.
And the Government's chief scientific adviser Patrick Vallance said the speed at which vaccines could be produced was the main limiting factor across the world.
With GP practices doing the majority of the vaccinations in Yorkshire they are well on course to meet the Government target of giving first doses to all care home residents and staff by next weekend.
But one medic in Doncaster said that with a faster and more consistent supply of the vaccines from central government they could have already got round all the over-70s in the borough and started on over-60s and over-50s.
Dr Richard Vautrey, a GP in Leeds and chair of the British Medical Association's GP committee, said groups of six or seven practices in the city were able to administer more than 1,000 vaccinations in a day or two of getting a crate of the Pfizer vaccine.
He said: "GPs are used to doing mass vaccination. If you give us a vaccine we'll give it to our patients and we just now want that in volumes, similar volumes almost on a daily basis.
"We see this is a real priority, it's just getting the vaccine which is the key and we would hope that that improves over the next two or three weeks, so that we get more vaccines and we can put on more clinics."
Dr Dean Eggitt, a Doncaster GP and chief executive officer of the borough's Local Medical Committee, said local teams were doing a "cracking job" to get the vaccine out to patients given the snowy weather.
But he said the supplies were not coming fast enough and that local practices "could have vaccinated quite a large proportion of our population if the vaccine was sat here ready to go".
He said: "I would imagine that we could quite easily be through a large proportion if not a majority proportion of our population if the vaccine was really ready for us to roll out."
On several occasions GPs had been given short notice by NHS bosses that a delivery was coming only to be told hours later to cancel all the bookings they had hastily arranged.
Describing one incident, he said: "We got the nod that some vaccine was coming. So everybody kicked into action, we started inviting hundreds of patients through. We gathered team members to say 'who can come in at short notice to run this clinic'.
"Everyone stuck their hands up, everyone was ready to go. We then got a phone call saying well actually it's being cancelled, can you step it down. So we started saying to staff members you don't need to turn up, phoning all the patients to say 'you don't need to come'.
"And then we got an offer saying 'well, actually if you do want some vaccine we might be able to get you something short notice, what do you want to do, do you want to put the clinic back on or not'.
"You can't have this toing and froing with the staff because the goodwill is going to go at some stage and then when you ask for volunteers, they're just not going to be there. We need consistency."
Dr Geetha Chandrasekaran, a GP in Halifax, said more than 10,000 doses have already been administered across Calderdale and that almost all care home residents will have had their jab by this weekend.
She said: "Our constraints at the moment are supply, if we had supply, we would all be out vaccinating, and we're all geared up to do that as well from a point of view of workforce, we have it all set up and we are ready to go, if we have the supply we would keep vaccinating."
She said local practices had done "exceptionally well" to deliver the doses they had been sent while still carrying out the winter flu vaccination and other services, adding: "We're a bit sad that we don't have the vaccines to be able to go out and do it, even though it was challenging to do it in the first place."
In the Downing Street press conference yesterday, Mr Johnson declined to say how many doses of vaccine were currently available but that supply depended on the capacity of the Pfizer and AstraZeneca factories to produce it and the batch testing approval process.
He said: "So we've got to get all that right. And what I can tell you is that we're using all the supply that we can possibly lay our hands on. The UK secured bigger supplies than any other country, and we're going to get them into people's arms as fast as possible."