The short answer is yes. For your car to be listed on RideLink, your car should meet all the legal requirements, including the minimum insurance and MOT required by British legislation.
Both a valid MOT and insurance are needed to guarantee that the car is in good condition. Having your own insurance policy is essential for avoiding messy and confusing situations for you, as well as the renter. For example, if the police pull over a renter while they are renting your car, their databases will reflect only if the vehicle has insurance or not. Having your own valid insurance allows the renter to continue his/her journey without interruption or hassle.