Boris Johnson confirmed the figures at a Downing Street press conference where he said the roll-out was well underway.
Provisional figures suggested more than 137,000 people were given the first injection in the first week. Of those, 108,000 were vaccinated in England.
The majority of the vaccines were administered to the over-80s, care home workers and NHS staff through more than 70 sites across the UK. GP-led centres have also begun administering jabs, with care homes next on the list.
The Pfizer/BioNTech vaccine is the first vaccine to be authorised for use by the medicines regulator the MHRA. Patients require two doses of the vaccine – 21 days apart – for the vaccine to be fully effective.