Permission cannot be withheld without reasonable cause. We all have the RIGHT to use our soverign airspace.
Reasonable cause would be the airspace operating at capacity, a figure which is known by the ATC unit, the UK Flow Management Unit, and Eurocontrol.
Note that because it's quiet when you call, that doesn't mean that the airspace hasn't just been at capacity for a given period, or is about to become extremely busy shortly. On the flightdeck you will have no way of knowing.
There is no reason however why pilots who make a transit request in good time (a minute or two to the boundary would not be 'in good time' in my book) should not be told straight away what the score is. Either to expect a clearance, to expect no clearance for the foreseeable future (with a short reason provided), or to expect a clearance in X minutes due to YYYYYY.
As BEagle says, there is a conduit to report any entry refusal to the CAA. Feel free to make use of it, but don't necessarily be surprised if quite often there is a legitimate case made as to why entry is refused. There's a responsibility placed on the ATC unit to provide justification in each case to the CAA or else face the consequences.
Personally I have never had any problems transitting Class D airspace, with flexibility being the key to a successful crossing, either by accepting a slight delay, or suggesting a different route to the controller. Building up an air picture and letting the controller know you have traffic in sight and are happy to pass behind/above/below etc also gives hard pressed controllers a little nudge to think about more options.
Nice to see that snobbery is alive and well though ... lo cost being classed as Chavairs. The gin soaked ex forces officers of the world living in their own little days of the British Empire are just as worthy of scorn
Dinosaurs
