The CAA delegates management of a particular piece of the UK's airspace to a particular ATS provider for the ATS provider to commerically exploit the airspace and maximise its revenues?
IN a nutshell... YES!
As the airspace was "given" as you say to a unit for the purpose of getting PUBLIC TRANSPORT FLIGHTS safely into the airways system, yes, it is they who have priority!!!
I won't bother quoting my MATS pt 2 but at the front it details priority of flights. Yes - you guessed it - VFR transits isn't at the top!!
If you feel you don't access to any Class D and THAT IS UNFAIR you should take it the units management and/or DAP.
For what it's worth the SRG man who sat in with me mentioned not giving too many zone transits when you are busy wth other things. Other things being a multitude of stuff.......but not VFR FIS'ers!
It is far easier to work a constant stream of IFR ins and outs than a few IFR's and a load of zone transits I can assure you.
Sorry - that's just the way it is.