OK... how much time do you want to sink into it?
If you want to do it "properly"
then there is only one way which is to pitch up a tent next to the school and fly 2x a day
If you want to do that, you ought to consider an airport with an ILS. The options within 2hrs of London are considerable, but I would suggest a 2hr drive is a very long way and you won't be much good for flying afterwards, never mind instrument flying for which you need to be as fresh as a cucumber to get any benefit from it.
Within a 1hr driving radius (and it hugely depends on where in London you live, because it can take 1hr just to get out of the damned place) you have Southend, Manston, Bournemouth. I know there are some well organised (if not cheap) schools at Bournemouth, but can't speak for the others.
That should give you a 90%+ despatch rate for instrument lessons. All have NDB approaches also. You can fly fake VOR approaches at various VORs, or a real one at Southampton (SAM) without landing there.
The IMCR is done wholly at very low altitudes (say 3000ft or lower, all OCAS) and in spring/summer icing won't be an issue at those, so no need for a de-iced plane. Anyway, if you are flying a de-iced plane and you start collecting serious ice, that would be the lesson over anyway.
You could also do it out of Shoreham, which is perhaps the next best thing. No ILS but 2 trains out of London will do it (I don't think there is a direct one anymore but there might be) and it has the NDB and GPS approaches and you can do fake VOR ones around SFD. Being coastal, it is fairly easy to get back in bad weather.
You can do the IMCR at a proper FTO too but frankly I think that is just a waste of money.
If you have no instrument skills at all then I suggest buying FSX and a cheap joystick, because you should never try to fly any procedure unless (a) you can fully understand the plate and (b) fly it on a sim. A sim saved me £thousands back in 2002 on the IMCR, but I never used one since.