Insurance is handled as part of the affiliation process between a club and the relevant national governing body (the British Baseball Federation or the British Softball Federation). It works in a slightly different way depending on whether it's baseball or softball:
Generally, it is softball leagues which affiliate and pay an insurance fee to the British Softball Federation. Going down the chain, clubs pay membership and insurance fees to their league, and players pay membership fees to their club, which includes annual insurance cover. The exceptions are tournament teams which don't play in a league but take part in BSF tournaments through the year. They will affiliate directly with the BSF, sometimes done through a tournament entry fee.
Baseball clubs, on the other hand, affiliate with the British Baseball Federation directly and pay an insurance fee in the process. Players then obtain insurance through membership with their club.
Both federations require that players be registered with their club on the British Softball or British Baseball websites as a condition of insurance. This is to make sure that we can identify who is insured in the event of a claim. These sites also contain information on the affiliation/payment process.
Find out more about insurance.