That is a poorly written/misleading statement by British Cycling and they going to lose the battle. In fact I can't see how the average cyclist will be worse off.

The full statement is here: http://researchbriefings.files.parliament.uk/.../SN04141/SN04141.pdf. Any claims less than £5000 will move a fixed tariff system based on doctors prognosis so you can definitely still get compensation for claims less than £5000. Overall it should be easier to legitimately claim minor injury compensation following an RTA because there are much clearer definitions of what gets paid when. Legally speaking however the move to tariffs does migrate claims less than £5000 to a different system hence it is technically correct the limit moves from £1k-£5k.