I regularly fly IFR in a single around the LTMA. You can fly IFR outside of controlled airspace, but generally your flight plan needs to conform to the standard routings published on the AIS website. From Cranfield, you'd need to file DCT BPK N601 DET DCT DVR L9 KONAN and until you were in Class A airspace you would be under a radar advisory service. You must still also comply with the 1500 foot rule so being IMC over central London on a heading direct to DET wouldn't be acceptable. A few times I've had to remind the controller "unable" when I've been given such clearances (or a climb to FL120 without oxygen).
Are you sure your "average" 172 is equipped to fly IFR in the LTMA? Mode S, second altimeter etc?