Stephensons, Uttoxeter, had a prototype Leyland Olympian, Q246 FVT (photo on Flickr - not mine -
here)
As of a year or so back, and I think it's still the case, Q plates still existed as pretty much a last resort for vehicles of uncertain parentage, although DVLA will do their best to issue an age appropriate registration.
If (say) a 1972 vehicle is imported from outside the UK, and some documentation can be produced from the country it was first registered in that proves it's a 1972 vehicle, then DVLA will allocate a 1972 registration number.
They accept quite a range of documents to prove the age of a vehicle, e.g. letter from manufacturer which ties a particular chassis / VIN number to an age.
In the case of classic vehicles, some historic vehicle organisations are authorised by DVLA to vouch for a vehicle that's been imported, or one that's been off the road for so long it's fallen out of the system and was off the books before SORN came along. (if possible, and if the vehicle's identity can be proved, the vehicle's original UK registration number will be reinstated.)
The rules have changed over time - at one point, if you registered a vehicle in a particular year, you got a registration for that year. There were (for example) a couple of London RTLs that got re-imported from Jersey in the 70s that got P suffix registrations (MGP 11P was one . Similarly, there were one or two 1970s coaches that for some reason never saw the light of day until the 1980s that got E - registrations (Brylaine Travel, Lincolnshire, ran E903 DRG for some years.)
And some of the AEC Swift / Merlins bought by London Transport in the late 60s managed to get a registration number a year or two newer than the buses were, as industrial relations problems prevented them entering service the year they were delivered.
I'm pretty sure you can't do that now.
I'm not sure if the owner of a vehicle offered a Q plate also has the option to buy an ageless registration number, either English (pre 1963) or the cheaper option of a N Ireland number...