I would say what you have inside your boots and trainers is your business.
In basic training there is a lot of running, jumping, carrying.... Runs can be short and very fast, or 8 to 10 miles at a good pace. A lot of people have problems with their knees because of this (Mine are still giving me problems and I left the Army 10 years ago)
If you have an existing foot problem then you need to be very careful that you don't do some permanent damage. Let the medical centre know about it when you start training and they may issue you with sorbathane insoles to help cushion from the pounding you're going to have to endure.
It doesn't stop after basic training though, normally when in camp in the UK or Germany you have 2 runs a week to maintain a basic level of fitness as well as your normall fitness tests. On top of this you may have more PT prior to a deployment or operational tour.
If you've already passed the medical then I don't think you've got much to worry about
Royal Engineers for 16 years