Assuming weather wasn't a factor:
From Stapleford, I'd route to the east of City, down to Mayfield VOR/DME (or Bewl Water if you want to see some sailboats), then for sightseeing purposes I'd head to Beachy Head, and slowly starting my climb to FL60 whilst following the coast, then once by St Catherine's Point, I would climb to FL105 whilst going direct to MP (NDB) (or directly south from SAM VOR/DME) to keep clear of the airways.
Then maybe come back the other way around London - just for a change? Ie: Head direct to Wycombe Airfield then head East on the north side of London Heathrow's zone.
Remember, FL10,500 doesn't exist... Its FL105! And you should definitely still be in sight of the surface at 10,500ft. The only thing you need to consider at that height / altitude / Flight Level is the fact that there is less oxygen up there, hence why 10,000ft is really the highest people will go VFR without oxygen, but according to the French, they want you to fly the proper FL according to the semi-circular rule which puts you 500ft higher.
Consider taking your passport if you need to divert to France, and also call them ahead telling them that you MAY divert to them due to weather. I've occasionally seen the isles completely in thick haze, whilst Cherbourg was bathed in glorious sunshine - keep that in mind!
But most of all - have an amazing flight, it is stunning!