I don't think any of us has given the OP a clear answer.
The route you propose from Banbury Reservoir to Canary Wharf follows the Lea Valley lakes. This used to be a common route for single engine. Some still do it, but because of the glide clear requirement, there is much debate about whether it's legal.
If you ask for that clearance from Thames Radar, you may well be granted it, but you may have some awkward questions to answer afterwards. Recently, I was in an aircraft that requested that route and Thames asked us if we were single or multi engine. (It was a twin.)
East along the Thames from London City to Rochester would allow you to glide clear into the Thames. Again, there is debate about whether that meets the requirements. I have flown single engine from Dartford QE2 Bridge to London City and back, along the Thames at a weekend when London City was closed. The clearance was requested and given. But, on a weekday, you (as talkdownman has made clear) are going to conflict with London City movements and that bit of your route may be a big problem to them.
Continuing South from Canary Wharf really doesn't give much option for glide clear. Greenwich, Lewisham, Catford and Bromley are congested areas.
I don't think your proposed route is reasonable on a weekday and the view of the City of London as you track the M25 is pretty good.
If you fly direct from VOR BPK to M25/A127 junction, a route I fly often in a single, you will get enough sightseeing to please the eye. If you overfly Stapleford ATZ at 2,400ft QNH there's no need to speak with them, or if you prefer, you can go just a little South of their ATZ. For radio, either turn it down and enjoy the view, or take a service from Farnborough Radar North. Follow the M25 to the Dartford QE2 bridge, then the river towards Rochester. Pay attention to Southend's airspace along the Thames, but they will almost certainly give you a clearance through their space on your way to Rochester, if you want to stick with the river.