In uk.transport.london Paul Corfield wrote:
The final slower option is to use the 473 bus from LCY to Stratford.
You get a level connection at Stratford Bus Station on the return leg
and a short connection across the Broadway on the outward leg.

http://www.londonbusroutes.net/times/473.htm

Thanks, the 473 looks like a good option. It only takes 20-30 mins, which
is probably quicker than lots of faffing at interchanges. I might give that
a go.

Theo