Arriva used to (until quite recently) run coaches on the Newcastle-Carlisle 685 route. They stopped because the ageing coaches were becoming increasingly unreliable.
Now they have 'buses' (albeit with leather seats) - but the passengers are unhappy.
As far as coaches and buses are concerned there are (in some cases - subtle) differences, but to me, coaches have plug doors and, usually, high floors, but, specifically are geared for higher cruising speeds (or lower engine noise at cruising speed) and may have more sound insulation.
Nobody would want to travel 300 miles in a Routemaster.
However, what we describe as a 'bus' could be fitted with 'coach' gearing (rear axle ratio or overdrive gearbox) but might need additional low ratios for steep hill gradeability. That shouldn't be a problem nowadays with multi-speed automatic gearboxes. I know that ZF were offering a seven speed wide-ratio Ecomat 7HP600 at least 20 years ago (though it was mainly intended for heavy commercial vehicles).
I don't know what current buses (or coaches) are using.
RE: Go North East - Latest