It's important to note that there isn't one 'Ambulance Service' (just as there isn't one 'Police Force'). There are many regional Ambulance Services, and they each have their own equipment and operating procedures. Some can accept OSGB GRs, some cannot.
Personally, I think it's a disgrace that the emergency services cannot universally accept the national mapping coordinate system (so much so that I'd sack anyone who specified an emergency response GIS that could not accept OSGB GRs), and they certainly shouldn't be charged to use OS mapping data. For all the nonsense about being an 'autonomous agency', a very large proportion of their money still comes from the taxpayer.