2 Donkeys has it spot on and London Inf or the likes of Thames and Farnborough are always very helpful an efficient in activating flight plans in the absence of ATC at an airfield.
The main reason for not leaving VFR and transferring to IFR is that you will save a hell of a lot of radio time if you don't have to file an airborne flight plan. It is better to have it in the system before you leave. (You can fax it to Heathrow or similar and then call them to check it is in before you take off).
The issue, in the weather conditions described, is to get a radar service as soon as you can after departure whether it be RAS or RIS. If you are leaving from an airfield that is not within range of a suitable station then you have to take the chance whether you are VFR or IFR