These vaccines are currently approved for use in the UK :Moderna (Spikevax), Pfizer/BioNTech (Comirnaty), Novavax (Nuvaxovid), AstraZeneca (Oxford), Janssen (Johnson & Johnson) and Valneva but you cannot usually choose which vaccine you have.
There are some groups of people which take certain vaccines as pregnant women, who are under 18 years or aged 75 or over and getting a seasonal booster dose or people had a severe allergic reaction to one of the common vaccines.