Hmm, this is a weird one too:

https://www.openstreetmap.org/directions?engine=fossgis_valhalla_bicycle&route=51.52976%2C0.00528%3B51.53409%2C-0.00654#map=15/51.5290/-0.0011&layers=N

Even if you start on the ramp and route to another part of the cycleway, it takes you off onto a road in between. Or start part way along:

https://www.openstreetmap.org/directions?engine=fossgis_valhalla_bicycle&route=51.5329%2C-0.0040%3B51.5341%2C-0.0065