From the UK COVID-19 vaccines delivery plan:
4.3 The government’s top priority is to ensure that everyone in cohorts 1-4 is offered the opportunity to receive their first dose of vaccination against COVID-19 by 15 February. It will likely take until Spring to offer the first dose of vaccination to the JCVI priority groups 1-9, with estimated cover of around 27 million people in England and 32 million people across the UK.
4.4 It is estimated that taken together, these at-risk groups account for 99% of all deaths from COVID-19 to date.
The UK is prioritising giving more people one dose of the vaccine, with the second dose given around 12 weeks later.
This BBC article on the vaccine rollout provides some useful context.
When will 32 million people in the UK have received a dose of a COVID-19 vaccine?
This question resolves when the UK government reports here that the cumulative number of people who have received a first dose of a COVID-19 vaccine across the UK reaches 32,000,000.
If there is a reporting lag, the question resolves on the date the vaccinations actually exceeded 32 million, rather than the date of the public report.