Please don't generalise. CB has hit the mark... If there is a problem with neighbouring airfields/units, the answer lies in liaison, not personal attack.
FACTS: Both sides work under slightly different interpretations of similar rules (right or wrong?), both work under slightly differing pressures, some have inflated egos, not everyone is the same.
... and Standard Noise believe it or not, similar priorities?
priorities that go along the lines of safety, expedition consistent with that safety, ond order
... regarding your specific scenario, the Sector Controller let the traffic off-route in the first place... to help? Swanwick (Mil) would have accepted the traffic assuming they would be able to handover the traffic as it approaches the destination... to help.
The traffic was, I presume, pre-noted ahead of arrival and it is that point you can express any concerns you have if it is inconvenient. I don't doubt you were "one-armed paper hanging" with the traffic already in the zone, but you may have left Swanwick (Mil) with little option and certainly no solution, what did you expect them to do with the traffic?... although I agree a freecall isn't helpful. (IMHO they do not have the capacity they used to have when at West Drayton?).
For once, I agree this is the sort of problem caused by the routing of GAT through
unregulated Class G airspace... but wake up to the facts, like it or not... it's happening more and more, wise or unwise it is not yet illegal, so ranting about it, and the people trying to make it work, is NOT the answer.
In the scenario, I believe everyone was trying to do what we do best i.e. help... This time it didn't work out for you... hopefully some lessons were learnt? Speaking to the Sector was the right action... did you speak to Swanwick(Mil) too? If this is a recurring problem, formulate an SOP, so then everyone knows what to expect and has options.