Hi,

Changing vehicle=no to motor_vehicle=no here may cause problems for other data consumers, as that's not what the signage means.

In this case, the signs visible in Bing's streetside imagery here ( https://www.openstreetmap.org/way/3528791 ) are the TSRGD diagram 953 variant "Route for use by buses and pedal cycles only". That translates to OSM access tagging as:
vehicle=no + bus=yes + bicycle=yes

Replacing vehicle=no with motor_vehicle=no implies carriage=yes. OSM-based routing for horse-drawn carriages may be somewhat niche (arguably, so is routing bus journeys after they have taken place), but we should tag to the best of our ability to reflect reality and shouldn't entertain changes which would potentially send more vulnerable road users like drivers of carriages along roads where they are prohibited.

I can see that you're trying to make a positive contribution to OSM and improve the experience of your fellow Busmiles.uk users, but you won't balance those two objectives if you ignore changeset comments.