Nimbus,
With regard to choice of which agency to call on the radio, don't forget that GA pilots have to make that very same choice on every flight in Class G!
(I'm not sure what you mean by "enroute frequency" in view of your question about which agency to call. It is possible that what I write below may be exactly what you do already, if so my apology for trying to teach you to suck eggs).
It sounds like in the particular circumstance you quoted, the best choice in Class G would probably be Farnborough Radar but without knowing your exact route I'm not certain. I'm sure you are aware that Benson can also offer a radar service, as do Brize Norton. Transitting GA routinely works those units as appropriate. All you would need to give is present position, altitude and route so it could be passed on to other traffic. I'm NOT suggesting you give up 130.4 altogether, btw.
Do emphasise that you would be going IMC because that is the whole point of the discussion, otherwise it's the usual rules of "See and avoid" in Class G.
GA pilots routing IFR / IMC near Farnborough are highly likely to be working them. ATC would treat you just like any other aircraft (hopefully you WILL appear on their radar) and they would advise other pilots working them of your presence. Obviously, it's your decision after calling them whether you stay on that frequency or change back to 130.4. If you become VMC and / or leave the area it would be great if you could call them back and say so. Safety improved for everyone, just a couple of quick calls.
Your profile says you have a PPL and fly IFR capable helicopters; there must be IMC rated / IR qualified pilots around your neck of the woods. Why not discuss this locally or ask for some local advice?
Thanks for at least discussing it here, some valuable inputs.
