Of course there are plenty of other places where you can learn to ring, and if you will only be in Cambridge for a short time you need to find somewhere else to continue learning. The traditional route to becoming a bell-ringer is to get in touch with the tower captain at a local church with bells and see whether one of the ringers there will be able to teach you. If not, he or she should advise you where else you might go. In most places lessons are provided free of charge, and bell-ringing can be a very low cost activity.
The first step would be to consult Dove’s Guide and identify a local church with bells and a practice night. There may be a link to contact details for a tower secretary, otherwise most churches have a website with helpful information. Make sure the practice is at a time when you can attend regularly, and take it from there. Don’t be afraid to turn up to listen and say hello.
Another option is to contact the Association of Ringing Teachers who will put you in touch with one of their members in your area.
If you can make an arrangement for someone to teach you, it may be that the available time each week is quite limited in which case it could be difficult to make rapid progress. If St Clement's is within reach there is always the option of coming here to improve your progress. Ask about other opportunities, and once you can ring a bell without assistance you will be made welcome at practices and can even visit other churches in the neighbourhood. A bell-ringing practice is organised with fairly short pieces of ringing so that there is something to suit everyone who is there. The more competent you get, the more you are able to join in. Expect to turn up on Sundays too, to take part in the service ringing.
In most places there is no requirement for the ringers to attend the services they ring for, but unless you are intending to go to them it would be a good idea to find out what the local tradition is.