I believe I read in Pooleys (don't have it in front of me, and information should be checked in the AIP anyway) that Heathrow won't allow any single-engined or light twin-engined aircraft in (don't know how they'd definte "light" with regard to the twin, but banning singles rules out the PA28).
Also, as FBW says, you'd need SVFR - remember, ATC don't have to give you this, it is entirely at their discretion, so even if you get permission to land, you may not get permission to enter the zone
Have to agree about big airports, though - I also asked my instructor to take me "somewhere big", and we went to Bournemouth - amazing to be sharing the runway with 737s!
FFF
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