I have found this image at last on the internet - there is only one available, and it accompanies a newspaper article in the Northern Echo about the Beamish Run for classic cars and motorcycles. The photo is ,alas, not captioned, and I have had to revert to trawling the list of runners to find a likely candidate.
The only likely car is a 1951 Alvis Special driven by William Wiggins. Does this ring a bell?
(I have checked DVLA records - the registration shows a grey-coloured car from 1957 with a 2.5-litre engine. As they say on WW2 US Navy films - "That is all")