Hi MT,
The UK is not the exception in this case. The majority, if not most, larger airports worldwide do not provide Ground Handling services to the airlines - for reasons of cost/benefit, expertise, hassle ... however you want to view it. Airport companies tend to stick to the terminal side of things, and the runways, taxiways, navaids like ILS, etc.
So its not so much that the Airport contracts the Ground handlers - the Airlines do, directly; there are pretty clearly defined boundaries as to who owns/does what. For example, the airport owns the airbridge, but they don't operate it - the airline does - through the handling agent. The airport won't own the pushback tug, nor the towbar, though they may provide in-ground power.
Fraport is among the exceptions. Why? Not sure. 'Frankfurt is different' is an oft applied motto for the airport, though. Everything is a lilttle different there!