The official name for no win no fee arrangements is Conditional Fee Agreement (CFA) and they will often deal with any type of case outside family or criminal law, they are probably best known for personal injury cases. You may be required to take out “after the event insurance” and it should be very easy to locate a firm that accepts CFA now that advertising is allowed in your local paper, yellow pages, on line, or by ringing around.
You may find some of your work is undertaken by Legal Executives rather than Solicitors but probably no more than in non CFA cases, a major advantage is that as has been said a CFA firm will not accept your case unless they believe there is a good chance of success which indicates the strength of your position.