Provisional figures published by the government show that 108,000 doses of the Pfizer/BioNTech vaccine had been delivered to at-risk patients in England, with the rest spread across Scotland, Wales and Northern Ireland.
A DHSC statement said the 'majority of the vaccines have been administered to the over-80s, care home workers and NHS staff through more than 70 sites across the UK'.
Around 50 'hospital hubs' began offering COVID-19 vaccination to care home staff, NHS workers and patients aged over 80 attending for outpatient appointments or being discharged from last week.
On Monday, NHS England said 'practices in more than 100 parts of the country are taking delivery of the vaccine today, with some kicking off their clinics this afternoon and the majority starting on Tuesday'.
An NHS England bulletin on Tuesday said 'hundreds' of primary care sites had begun receiving vaccine deliveries.
The NHS has previously suggested that 280 GP designated sites were due to go live in the first wave of rollout of the COVID-19 vaccination programme in England - meaning that with each site expected to deliver 975 doses within a 3.5-day window, around 273,000 doses could be administered by primary care sites alone by the end of the week beginning 14 December.
However, GPonline reported last week that some sites had been forced to pull out of delivering vaccinations because they were unable to accommodate a requirement for 15-minute observation of patients after vaccination following allergic reactions.
Other GP sites reported being forced to reorganise appointments booked with patients for vaccination at the last minute because deliveries of vaccine and other equipment to vaccination sites were delayed.
The government has said it will start publishing weekly updates from 21 December on vaccinations delivered.
It said that as further batches of vaccine are delivered to the UK and the number of sites administering the vaccine rises over the coming weeks, 'the rate of vaccinations will increase'.
Health and social care secretary Matt Hancock said: 'Thanks to the hard work of the NHS across the UK, over 137,000 people have already received the first dose of the coronavirus vaccine.
'This is just the start and we will steadily expand our vaccination programme - ultimately helping everyone get back to normal life.'