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Very few spots in London because the first 12 miles are in Tunnel, St Pancras, Stratford International & Rainham are probably your best bets. Dagenham dock might work for trains coming out of the tunnel.
You could try the RSPB reserve at Rainham Marshes; the "boardwalk" part of the circumference footpath is extremely close to the flyover section of HS1 although you'll need to plan your angles carefully because of a couple of National Grid lines immediately behind the viaduct...
At least the sunlight will be behind you virtually all day...