The OSRM debug map shows that Fox Talbot Close is missing from the bike routing graph:
https://map.project-osrm.org/debug/bike.html#19.36/51.45283/-0.98215

Maybe OSRM didn’t update the bicycle routing graph yet.

Maybe access=permissive is treated like access=private for bike routing. If that’s the case, it should be reported to the OSRM developers as that doesn’t make sense.