mm_flynn's answers are good.
This is not a stupid question at all.
It is a very good illustration of how the utility value of flying goes in the bin the moment the cloudbase goes below about 1000ft AGL. Most "GA" airfields have no instrument approaches and only an ILS is going to get you below 400ft anyway.
A departure in these conditions is easy, for an instrument-competent pilot. It is purely a risk management thingy - if you have climbed into IMC and then get an engine failure, you may have only a few hundred feet in which you will be visual, to find a field.
Enroute is also no problem at all. Practically nobody else will be flying, so just drill along at 2300ft or whatever, below the LTMA. If you can get a radar service (Farnborough) so much the better. Nav would be GPS, obviously.
It is landing that's the fun bit. Only a brave pilot would do a DIY cloudbreak in a 400ft cloudbase. Such an approach would require very careful preplanning with the 1:25k O/Survey map and IMHO would be daft to fly without testing it first in VMC, and would require a general lack of obstructions in the vicinity. I would not do it down to 400ft, except if a descent is possible over the sea and the runway starts more or less on the beach. A 600ft decision height is much better. The procedure design is in any case critical and various things need to be done exactly right. For starters, you will be creating user waypoints in the GPS and if somebody else flying with that GPS changes them ..... so a VOR/DME backup on the waypoints is IMHO essential. This is not for amateurs. And it is illegal in an N-reg plane (reference: FAR 91.175) worldwide (IMHO).
Statistically, OVC004 is rare but OVC008 is much more common (UK warm front weather). A GPS approach would work fine for OVC008, but various stupid issues prevent them being adopted at places like Elstree.