You can't lay the floor at the same time as a strip foundation coz you need to build the walls up to DPC first.
The old scrumpy lad is right Mark, except that he has said strip foundation instead of trench fill foundation.
Dig and concrete founds, brickwork or block work to footings, blinded MOT to sub floor, DPM over and turned up footings and lapped over top, then concrete floor,
Regard foundation depth. We quote.
The depth to the underside of foundations on clay soils should not be less than 0.75m on low shrinkage clay soils, 0.9m on medium shrinkage clay soils and 1.0m on high shrinkage clay soils, although these depths may need to be increased in order to transfer the loading onto satisfactory ground, or where there are trees etc, nearby..
Regard foundation width. Your loading is approx 16.00 KN/lin metre and providing your setting out is very accurate and it is firm clay we would go 450mm wide.
We are not saying do not use strip footings, but if you do you will need 600mm wide width. We sometimes use a raft, but we ring beam the perimeter toe and mesh the slab.
One other point. on a garage we would not go cavity wall