For London, wouldn't Clarkes or Kings Ferry be adequate?
I'd say it depends. The King Ferry yard in Gillingham is small and pretty full under normal circumstances, and in "normal times", they tended to cover NatEx work as an extension of the now much reduced commuter services. Their "NatEx" at Dover is, as far as I recall, rented space, and even further still for London work. The Hounslow base for Airport work is also on that license, but I don't know how large it is and what they could fit.
I've never seen the yard at Lower Sydenham (Clarkes) to know how large it is, but again, there is/was a fairly sizeable private hire fleet to be stored there. Streetview suggests it is long and thin, and I'd estimate fairly full.
Incidentally, the Clarkes commuter services and LSP (London Service Permits) have been formally transferred to Kings Ferry. Whether this is a tidying up exercise so that all scheduled work is on the KF license I don't know, but all the acquisitions (KF, Clarkes and the Hampshire ops) are now marketing themselves as National Express Transport Solutions.