The most reliable, generally available, is Cafedirect. They do all sorts of coffee - you haven't said if you wanted instant, ground or beans.
Clipper do a decent instant coffee (they are better known for their tea)
My own favourite - stocked by our local wholefood co-op is Equal Exchange, but they are harder to track down.
Have you looked on the Traidcraft site? www.traidcraft.co.uk/
A lot of churches, some charity shops, and others sell Traidcraft stuff - it can be a bit hit-and-miss, but worth seeing if there is one near you.
And thank you for joining the movement - I have been involved in the Fairtrade movement for about 35 years now. We have come a long way! Dilemmas remain, life isn't perfect, but taking small steps to do the best we can do today, is very worthwhile.