This might be an issue with the routing software, but all three engines provided on the OSM site fail to plot a pedestrian route along the northern side of this stretch of New Oxford Street:

1) Valhalla:
https://www.openstreetmap.org/directions?engine=fossgis_valhalla_foot&route=51.51754%2C-0.12453%3B51.51697%2C-0.12679#map=19/51.51735/-0.12565

2) OSRM:
https://www.openstreetmap.org/directions?engine=fossgis_osrm_foot&route=51.51754%2C-0.12453%3B51.51697%2C-0.12679#map=19/51.51722/-0.12566

3) Graphhopper:
https://www.openstreetmap.org/directions?engine=graphhopper_foot&route=51.51754%2C-0.12453%3B51.51697%2C-0.12679#map=19/51.51734/-0.12586