Certain types of British Cycling membership do include third-party liability insurance. However, keep in mind that you will not be covered for any liability to a fellow British Cycling member during any race, time trial or timed event, even if you have race membership.
CTC (Cycling UK) membership does include third-party liability cover, but this does not cover you during any races or timed events.
Compare the cost of Cycling UK liability cover and British Cycling liability cover with Laka's cycling liability cover.
Price quoted from British Cycling displays the British Cycling Ride Membership 12 month package. This membership package contains other benefits. Cycling UK quote based on annual full adult membership. This membership package contains other benefits. This comparison considers the cost of memberships, it does not consider any benefits which may or may not form part of a membership. Rates are illustrative; you must visit other sites to obtain a full quote. All quotes are correct as on 06/07/2020.