PAD-0
Oh! OK, so the url from the address bar, not from the ‘share’ panel!

When I tried earlier, the problem persisted using ‘OSM Directions’ (i.e. a route was generated via Coxbench, However, upon revisiting to do as you asked, I was surprised to see that you had been able to obtain the result one would anticipate. And further surprised that, on repeating exactly what I had done earlier today, that so was I! 

As shown here:
https://www.openstreetmap.org/directions?engine=fossgis_osrm_foot&route=52.9706%2C-1.4258%3B52.9734%2C-1.4588

So something seems to have changed.

In the app used to create the route that highlighted the issue, the problem persists, but I’d imagine it will until such time as its OSM data is updated.

I’m happy to bow out here!

Thank you.