As part of their centenary celebrations, the BBC have put a large number of previously unavailable old television reports online at BBC Rewind, most of which seem to come from their regional news programmes so won't have been broadcast outside those areas at all and in any case probably haven't been repeated since.
Search is a bit hit and miss and just seems to rely on hitting the right keyword as a generic search for motor racing also brought up stuff about pigeons! There seems to be a rich vein of reports from BBC Northern Ireland in particular, with quite a bit on rallying, but I also spotted some interviews with a couple of young chaps called Martin Donnelly and Eddie Irvine - I wonder what happened to them?
This is something of a gem, though, a February 1968 report from BBC South Today on the forthcoming establishment of the new motor racing circuit at Thruxton. An Alvis negotiating the circuit - driver and passenger both with lit ciggies! - and an interview afterwards:
No commentary on these two, but here's Stirling's Cooper being fettled in Rob Walker's garage in 1959 - Rob himself in the background:
And Stirling taking his IAM Advanced Driving Test, also 1959:
Preview of the 1953 TT from BBC Newsreel - Raymond Baxter at the microphone, interviewing Moss, Wharton and Parnell:
And the race itself - again no commentary, but filmed all round the circuit:
Graham Hill and Paddy Hopkirk (plus showjumper David Broome and 'Lord Ted' Dexter) in Northern Ireland in 1973:
Preview of the Birmingham Parade, Midlands Today, October 1978 - interview with Martin Hone, who does a lap of the course in a D-type. Plus a rather sceptical senior police officer who doesn't think cars will ever race on the streets of Birmingham:
Feel free to add any others you find below - happy hunting!