We have stayed at the CC site at Abbey Wood which is on a direct line into Charing Cross. There is another CC site at Crystal Palace which is on a bus route into Central London.
We stayed at the Lee Valley site.. bus stops outside the site short journey to the tube station.
Nice walks along the nearby canal, I don't think it's the nearest but no hassle traveling into the city.
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Our local site is beautiful. Its the C&CC club site at Hertford, and there are two railway lines from there into London. I would certainly recommend it.