The "amazing constellation" of doctors, nurses, local authorities, armed forces, pharmacies and volunteers was praised by Prime Minister Boris Johnson for "steadily building up that immunity" as the national total given a first dose approached four million this weekend.
And in Yorkshire, one of the regions which has seen the highest proportion of vulnerable people vaccinated, community teams have continued to administer the jab in large numbers despite the recent snow.
GPs have described having to respond quickly when a delivery of the Pfizer vaccine arrives to ensure all 1,000 doses can be injected into people's arms within a day or two.
Any spare doses made available when recipients don't turn up or can't get to their appointment are given to frontline health and social care staff.
And medics say they have been able to make each crate reach more patients after discovering a vial of the Pfizer vaccine could be used for six doses rather than five.
Sam Prince, Executive Director of Operations at Leeds Community Healthcare and one of those leading the vaccine roll-out in Leeds, told The Yorkshire Post she was "delighted with the way it is going".
She described an "overwhelming response" from current and former staff to meet the Government's target of vaccinating all care home residents by January 24 and all over-70s by mid-February.
She said: "It has been very much a complete system effort, it has been everyone working together. It has been a very good collective 'team Leeds' effort.
"When we've had snow in the last two weeks there have been no issues in getting gritters out, it was just a case of getting together and saying 'let's do this'."
Leeds was one of 50 cities opening a vaccine hub - at the Thackray Museum at St James's Hospital - within days of the Pfizer vaccine getting approval. On December 15 three primary care networks started administering the jab and 19 are now live.
On January 11 a staff hub opened at The Mount in the Woodhouse area of the city, focusing on vaccinating staff but also inpatients and high-risk patients. It is hoped that a vaccination centre will be opened at Elland Road in February.
The task of vaccinating has been made more challenging by the two snowstorms that have made many roads in Yorkshire impassable in recent days.
In Bradford, the council’s Emergency Management Team commandeered 4X4 vehicles from its fleet and arranged drivers to make sure that COVID-19 vaccines could continue to be delivered, patients could return home and NHS and care workers were able to get to their shifts.
Emergency Management and Highways staff transported vaccines from Keighley to Huddersfield where they were urgently required.
Dr Geetha Chandrasekaran, a GP in Halifax, said her colleagues in Calderdale had done "exceptionally well" to have almost covered all care home residents by this weekend.
She said: "Athough we're delivering it in general practice and we're at the forefront of the delivery, we've had quite a lot of support from our other partner organisations like the local authority.
"For example gritting roads, it seems an insignificant part but it all plays a massive part in what we can deliver, because we wouldn't be able to do it without all our partner organisations and the volunteers who have come forward to help us with the programme."
Doncaster Dean Eggitt said: "The roads are pretty treacherous, some staff members have stayed at home because they live a good 30 or 40 miles away and haven't been able to get in.
"Those staff members who have got in have either driven here or put on a pair of boots and come in. We've thankfully managed to continue to keep GP surgeries up and running as usual and vaccination clinics are up and running as usual so in the moment, nothing's stopping us."
At his Downing Street press conference on Friday Prime Minister Boris Johnson paid tribute to the areas where vaccination teams have protected more than 80 per cent of their care home residents.
He specifically mentioned 'North West Lincolnshire' but is thought to have meant North East Lincolnshire as the area he described doesn't exist.
The PM said: "And it’s thanks to that amazing constellation of the vaccination teams: doctors and nurses armed forces, local authorities, pharmacies and volunteers that we are steadily building up that immunity, that protection for the vulnerable, for the NHS and for us all.
"So, when the call comes, please do get a jab and, in the meantime, stay at home, protect the NHS and save lives."