I envy your route. Stratford Broadway, Mile End Road, Aldgate one way system, Hyde Park Corner and Shepherd's Bush roundabout stack the odds too high. keep to the Fen Causeway
I queried the Transport for London journey planner for your commute and it says you can do it in 1h57m (if you can do that 10 times a week you're ready for professional cycling ;-) and it suggests crossing Central London along "my route". You should check it out, it gives you a nice PDF map of your route. Nothing is 'mere'. — Richard P. Feynman
I think your route is probably one of those all-round-the-houses tourist specials that Britain specialises in cos we don't want to encourage cycle use.
Any other route is simply impractical, there are no E-W green corridors to follow. I have to cross the R Lee over Stratford Broadway - absolutely no choice, which pushes me onto Mile End Road, into Aldgate one way.
All traffic at the West end of london roughly in the direction I'm going goes through Marble Arch or Hyde park corner. There is simply no avoiding both. keep to the Fen Causeway
That'd also put me onto the euston road at some point. Do I look suicidal ? keep to the Fen Causeway