Quite a common situation over central London - it's been discussed here a few times before.
London City (Class D) controllers can, perfectly legally, clear a single-engined aircraft to fly through their zone, right across the centre of London, but only up to 2400' (above that is the London TMA, which is Class A). It's very unlikely that any single-engined aircraft could accept this clearance legally, though, and for that reason some City controllers have said on these forums that they won't offer this clearance in the first place.
Remember that obeying the rules of the air and flying safely is always the pilot's responsibility, and you can always refuse an instruction from ATC if you don't believe the instruction is safe and legal.
FFF
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