I remember my source saying it was Bedford-engined, not Vauxhall-engined but who knows.
Bedfords were built by Vauxhall, so Bedford engines were
technically Vauxhall engines. 3,298 cc sounds terribly large for a Vauxhall-branded car of the period, so it was probably sourced from a Bedford truck and Groves just entered it as a 'Vauxhall' special for some reason or another. (Regulations? Made more sense for a race car?)
It also seems the car had a name, as per my original question, but I have no idea what this was...
I agree that it must've had a nickname. Script reading "[___?___] Special" is visible in the puzzle image, as well as in one of the images I posted. The first word is too blurry to make out, but it's clearly not 'Vauxhall' or 'Bedford.'
'Wicked Special' maybe?