You can but you’ll find that the Taster Sessions, certainly at Newport are booked out for at least 6 weeks. Winter is the worst time to be doing track induction – track racing season is in full swing so the evenings are usually given over to race meets and all the training sessions for accredited riders are full.
But yes, once you manage to find a session, you just turn up and for about £15 you get an hour with a coach, bike hire and shoe hire (if necessary) are included. There won’t be much in the way of training, it’ll simply be getting you used to the track, going higher up it and maybe a bit of paceline work and a few sprints if there’s time and everyone is feeling confident.
http://www.newport.gov.uk/_dc/index.cfm?fuseaction=leisure.centres&contentid=devxp001384 for Newport
http://www.nationalcyclingcentre.com/ for Manchester