There's now a national registry where you can sign up to potentially be contacted by any vaccine trials that think they can use you:
https://www.nhs.uk/conditions/coronavirus-covid-19/research/coronavirus-vaccine-research/Doesn't commit you to anything except allowing researchers to get in touch.
Or some people might want to apply direct to the Sheffield branch of the Oxford vaccine trials:
https://covid19vaccinetrial.co.uk/participate-sheffieldThey're particularly looking for folks who may have higher exposure:
Recruitment of those with likely higher exposure to SARS-CoV-2 will be prioritised, in order to increase the likelihood of obtaining efficacy endpoints in the context of a waning epidemic. These priority groups will mainly consist of, but are not limited to, COVID-19 patient facing frontline healthcare workers (e.g. those working in ICU, A&E, COVID-19 wards, Paramedics, Care Homes, GP COVID-19 hubs, dentists, COVID-19 testing centres), non-healthcare staff working in COVID-19 clinical areas (e.g. hospital porters, receptionists, cleaners and others working in hospital environments), and other public facing keyworkers with no access to personal protective equipment, amongst others.