The UK government has committed to offer a first COVID-19 vaccine dose to all those in the top 4 priority groups recommended by the Joint Committee of Vaccination and Immunisation (JCVI) by 15th February. These groups contain about 15 million people, and account for 88% of COVID-19 fatalities (source, table 2).
As of 11th January, about 2.2 million people across the UK have been vaccinated. But more than 13 million people will need to receive jabs in the next five weeks. In a BBC article on the vaccine rollout, the UK's chief medical adviser, Prof Chris Whitty, has described such a timetable as "realistic but not easy".
Some data on the progress of the vaccine rollout is available from the UK government.
How many people in the UK will have received a dose of a COVID-19 vaccine by 15th February?
This question resolves according to the UK government dashboard.
In particular, the question resolves as the "15-02-2021" value of the "United Kingdom 1st dose total" column in the "data" section of the "People who have received vaccinations, by report date (daily)" section.