This version, from 1945, was the first episode that was filmed. It's pretty fascinating.
THE B.B.C. BRAINS TRUST ANSWERING "ANY QUESTIONS?" Reel 1
For the rest of it: Part 2, Part 3.
There are a few rather slow moments in these videos, I'll admit (this is clearly an age before intellectuals learned to play to the camera, but I find this makes them all the more charming).
As a general comment, I think that most of the participants come across rather well, except for C.E.M. Joad, who seems a bit of a reactionary loudmouth. (His answer to the question about 'what makes a happy marriage' in part one might be partly explained by his own experiences in this area.) Both Jennie Lee (a key figure in the foundation of one of my present employers, the Open University, among other achievements) and Julian Huxley do, at least in my view, especially well.
Other interesting things I then ran across while hanging around the Pathé site were:
1. A fascinating documentary about women's emancipation in Britain, probably from the early 1970s (judging by the reference at the end to Arthur Marwick -- also of the Open University -- as academic consultant). It's terribly old-fashioned in terms of its voice-over (not that this is a bad thing...); however, the images are fascinating.
EMANCIPATION OF WOMEN
2. A 1961 documentary entitled 'Beat School' about Burgess Hill school, at which students were allowed to do...well, essentially what they wanted to. Including -- gasp -- smoking and listening to records. Smoking, after all, 'calms the nerves'.