About 140,000 people in the UK have been vaccinated so far

An update to the vaccine situation in the UK after the rollout on 8 December

There are 137,897 people that have received the first dose of the Pfizer vaccine so far across the UK, with lawmaker, Nadhim Zahawi, tweeting out that:

A really good start to the vaccination program. It’s been 7 days and we have done: England: 108,000 Wales: 7,897 Northern Ireland: 4,000. Scotland: 18,000 U.K Total 137,897. That number will increase as we have operationalised hundreds of PCN (primary care networks)

The number is going to pick up once the procedures are standardised and more vaccines are introduced to the general public. But this serves as a reminder that it is going to take a long time for this to have a major impact on the health crisis.

There are more than 52 million adults in the UK so while the vaccination program has kicked off, this weekly figure is still far too low for now.
Also, this is just the first dose of the Pfizer vaccine. Those who had it will require a second dose after 21 days. So, that may yet double any expected timeline.