I want to add a 2nd storey over the garage. Will the 300mm slab foundation be adequate?

The foundation is unlikely to be suitable as it was only designed to support a single-storey garage, not one combined with a 2nd storey. When your designer has completed the Planning drawings, appoint a Structural Engineer. Inspection holes could then be dug to determine the suitability of the foundations. The engineer will then advise whether the slab can be reinforced or whether it would be more cost-effective to demolish the slab and start from scratch. Bear in mind that if you intend to convert the garage to a habitable room, the current floor is unlikely to have sufficient insulation to pass Building Regulations.