Tillerman answered yes, and there is solid evidence on his side. Wikipedia shows Erith in Greater London and if that isn't categorical enough then you can get there on an Oyster card, so it is officially within the remit of London Transport.
But it doesn't feel like London.
You can walk on the Thames path for five or even ten minutes before seeing another walker. And then they say "good morning", sometimes even unprompted. Real Londoner's jaws are at this moment slack, as no Londoner spontaneously acknowledges another while travelling.
What's more you can't see the Shard and how can you still be in London and not see the Shard?
It feels very different from urban populated London. The landscape seems inhuman, empty of people, where you can hear the throb of heavy machinery and the tweet of birds but not much else.
The great works of Joseph Bazelgette created the network of tunnels that transports London's sewage away from the centre down to the city's borders, the wastelands of the estuary.
And as you walk upriver passing the Erith Marshes you reach the Crossness Pumping Station and its equivalent on the northern bank:
Great Stink never really left, it just got transported for life.