OK, I'm following you now. The software takes the coordinates from the photo and reverse geocodes an address for it.

It's very much a "it depends" question. OSM itself doesn't provide any geocoding (just the data for others to), so we'd have to work out what Photo Mechanic uses, and then find out what interval that updates its data.

This website uses Nominatim, with very up to date data.

The good news is looking up the coordinates you provided in OSMs Nominatim now works as it should. So it's only a matter of time until it finds downstream to Photo Mechanic.

https://nominatim.openstreetmap.org/ui/search.html?q=51.394217%2C+-0.506700

For Grove Road you won't be able to get to address precision as that data simply doesn't exist in OSM yet. but it should give road level accuracy.
See: 

51.39371, -0.50930
https://www.openstreetmap.org/?mlat=51.39371&mlon=-0.50930#map=19/51.39371/-0.50930

https://nominatim.openstreetmap.org/ui/search.html?q=51.39371%2C+-0.50930