It might be possible to get car insurance in Florida with a UK driving license but it is likely that the insurance company that would provide the coverage would want you to obtain a Florida driver's license within a reasonable amount of time, usually 30 days. Also many insurance companies do not permit policies to be shorter than 6 months this will be another obstacle in finding auto insurance.

If you plan to visit Florida 4 months every year, contact the Florida's DMV for information about if you will have to obtain a state's driver's license or how to retain it when you leave and return. They might also have more information on how to obtain affordable auto insurance since they are likely to work British visitors often with this matter.