Having visited LTCC and Swanwick and seen how busy these folks are, I can understand the reluctance to let slow-moving VFR flights through at peak times.
I really cannot complain about the attitude of any of the controllers I've spoken to.
On every occasion I've asked for a transit of Stansted or Luton in the past couple of years, I've been given it - and very helpful service too.
Thames Radar have always been courteous and helpful - although on occasions they've refused service because of volume of traffic when I've been outside their zone.
I think the key is in FD's post - don't bother to ask for a "corner-cutting" that will only save you a few minutes.
And: listen first, and if it's extremely busy, don't even bother to call. When you do call, know what to say and do it briskly and clearly (and no more than the information the controller needs).
If you want a transit that will save you a LOT of complicated routing, and then if it's refused with no apparent reason, fill in that CHIRP-like form and send it off. I don't think you'll get to send in many.
I have some personal beefs (don't we all!), like why UK airways are almost exclusively Class A , particularly that absurd airway from Southampton to the Channel Islands. There must be all of one aircraft regularly using the airspace between FL035 and FL100 on that route, so all the VFR flights have to wind their way round Cherbourg (and risk getting caught up in the latest French ZITs and ZOTs). But those aren't down to the ATCOs.