It's normal for single engines to follow approximately the M25 motorway around N-E London, not above 2,500 ft, (I go for 2,200, to miss the 2,400 ft lot and the 2,000 ft round number types) and to speak to Thames Radar even if you are just outside the zone. Keep a good lookout as it's a busy VFR route.
From the ground at City Airport, you do see a single engine bumbling along from time to time, especially at weekends when the tower and airport is closed, which I've always assumed is a breach of the Land Clear requirements as there's just nowhere to put down, and even the City Zone has an upper ceiling of 3,000 ft. As a last ditch in the event of an engine failure you can always plan to put it in the River Thames, but that doesn't suit your routing.
VRP Isle of Dogs is for helicopters on their route H4 which follows the river.
Last edited by WHBM; 7th Sep 2015 at 14:14.