It's usually possible to get handled by a flying club at larger airports - I've certainly been handled by BCFT at Bournemouth, on the other hand it was BCFT that I was visiting.
But yes, a few airports manage to be extremely obstructive to private traffic. Edinburgh is for example, completely unuseable - leaving a visitor who wants to fly into the city at night or when expecting to require an IAP, taking the train from either Prestwick or Dundee.
I can't see however why legally these are restrictive practices - in the UK at-least. Virtually all British airports/airfields are in the private sector, so surely the company or personal owning and operating the airport has every right to decide who they have as tenants or subcontractors.
A nuisance, yes. Morally dubious, yes. Shooting themselves in the foot, quite possibly. But illegal, I don't think so.
G