Man of Honour
Gyms down here seem to be ~£35 pm so that's what £400 ish a year? A half decent bike is about a grand but will last forever.
Nobody ever needs to buy a £1000 bike just in order to cycle for general fitness and health! Those that do are simply owning more money than sense!
Plus your local youth will probably nick it anyway
I said it before and I'll say it again because it's worth saying again, Calisthenics costs next to nothing, can be done anywhere and will help you not only lose weight, but gain muscle mass and get a lean physique once the body fat percentage is lowered. It's also a lot more fun than using static machines at the gym, also more difficult/rewarding. You will end up with greater functional strength and mobility than someone who just does machines and weights.