The Fisher House story says that there is a Fisher House in every major US Forces medical facility.
UK plc has one Forces medical facility left, at Headley Court in Surrey, which can take comparatively few inpatients, although I have heard that there will be something akin to Portakabin accommodation there soon to increase its capacity.
The injured returning from points East who need long-term accommodation could be housed at Haslar, which, despite the antipathy of the Army is a very pleasant, quiet facility. It would be relatively easy to convert some of it to provide all the respite accommodation that the injured and their families might require, but it is an expensive place to run.
Move Headley's business to Haslar, thus losing the need to pay for Headley to balance the expense of running Haslar as a military unit again. Won't happen, because the gong seekers at the MOD just don't have the imagination or loyalty to put their people first.