The Cabinet minister also raised hopes that 100 million doses of a second vaccine are soon going to be “heading our way” to defeat the Covid-19 pandemic.
Like Boris Johnson, he did not repeat suggestions by Health Secretary Matt Hancock and Commons Leader Jacob Rees-Mogg that Brexit meant Britain got the vaccine first, ahead of the EU and US.
But he told LBC Radio: “I just reckon we have got the very best people in this country and we have obviously got the best medical regulators, much better than the French have, much better than the Belgians have, much better than the Americans have.
“That does not surprise me at all because we are a much better country than every single one of them.”
Pressed again whether Brexit helped, he added: “Just being able to get on with things, deliver it and the brilliant people in our medical regulator making it happen means that people in this country are going to be the first ones in the western world, in the world, to get that Pfizer vaccine, real competitive advantage.
“It’s down to those brilliant, brilliant clinicians in the regulator who have made it happen so fast.
“Our thanks go out to them because by doing what they have done they are going to have saved lives.”
Mr Sharma tweeted: “The UK was the first country to sign a deal with Pfizer/BioNTech – now we will be the first to deploy their vaccine
“To everyone involved in this breakthrough: thank you.
“In years to come, we will remember this moment as the day the UK led humanity’s charge against this disease.”
Mr Michaelis responded: “Why is it so difficult to recognize this important step forward as a great international effort and success. I really don’t think this is a national story. In spite of the German company BioNTech having made a crucial contribution this is European and transatlantic.”
Mr Williamson also hailed the “promising progress” of the jab being developed by Oxford University and pharmaceutical giant AstraZeneca.
Asked on Sky News if Britain could now avoid a third lockdown in the New Year, Mr Williamson told Sky News: “None of us want to see a national lockdown and none of us expect to see a national lockdown.
“With the fact that we are going to be rolling out a vaccine, the Pfizer vaccine, before Christmas and we have had such promising progress on the AstraZeneca/University of Oxford vaccine, with 100 million doses of that vaccine going to be heading our way once it’s got regulatory approval, I’ve every confidence that we can see the light at the end of the tunnel.”
However, he also urged people to continue to take the “responsible approach” of following social distancing and self-isolation rules to avoid a new surge in cases and tougher restrictions being imposed.
The regulator approved the Pfizer jab in just nine days of being formally asked to consider it as it had been carrying out a rolling review of of the vaccine for weeks as data came in from trials in a pioneering assessment method to avoid delays which can cost thousands of lives.
This vaccine is set to be administered to patients from next week, with 800,000 doses being shipped over in a first wave from the manufacturing site in Belgium.
The Oxford vaccine was submitted to the regulator more recently but if it followed a similar timescale to Pfizer it could be given the green light soon unless further information is required to do so.
The Pfizer jab has to be stored at minus 70Cand so is more difficult to use in care homes and other smaller site than the Oxford vaccine would be.
If the latter is approved, it will also be easier to provide a very high level of supplies as the Government has ordered 100 million doses, compared to 40 million of the Pfizer model.
The Oxford vaccine has faced questions over how effective it is after two trials, one with a half first dose, came up with different results, but they are expected to be answered in a paper with the latest data set to be published shortly.
Fifty hospitals across the country including seven in London were preparing to start vaccinating staff and patients.
Those in the capital include Croydon, Kings College Hospital and its sister hospital Princess Royal in Orpington, the Royal Free, Guy’s and St Thomas’, St George’s and University College Hospitals.
Health chiefs are aiming to vaccinate five million Londoners by April, provided enough doses can be supplied.
A series of mega-vaccination centres will be set up, as well as dozens of smaller ones scattered around the city.
Regulators around the world are under intense pressure to follow Britain in approving a Covid vaccine jab.
In America, Health Secretary Alex Azar welcomed the UK go-ahead for the Pfizer vaccine.
“This should be very reassuring. An independent regulatory authority in another country has found this vaccine to be safe and effective for use,” he told Fox Business Network.
Donald Trump, though, is reported to be furious that the American regulators had been slower than those across the Atlantic.
The British approval is likely to “put a little pressure on” US regulators to move swiftly, said Kirsten Hokeness, an immunology and virology expert at Bryant University in Rhode Island.
In Australia, regulators have been told “to put away their swimsuits and towels and to work as quickly as we can”, with the plan still only to start vaccinations in March.
John Skerritt, head of Australia’s Therapeutic Goods Administration said it would likely complete its review by “late January” and has told staff not to plan a holiday to get the work done.
“My staff have been told to put away their swimsuits and towels and to work as quickly as we can but also in significant depth,” he said.
Pfizer’s is one of the four COVID-19 vaccines Australia has agreed to buy, including from Novavax, AstraZeneca and CSL Ltd should trials prove successful.
Health Minister Greg Hunt said the January timetable does not accelerate plans to begin vaccinations.
“We are on track for first vaccinations beginning with our health workers and our aged care residents subject to approvals in March,” he said.
The European Medicines Agency has defended its timetable for approving vaccines, arguing it is more appropriate than the faster system adopted by the MHRA.