Are you sure your "average" 172 is equipped to fly IFR in the LTMA? Mode S, second altimeter etc?
Probably not. I just used that as an example. I fly an Archer III which does have Dual Altimeters, Mode S etc...
N601 is only available from FL090 and above. Is a climb from Cranfield to FL090 by BPK possible in this sort of A/C?