The interview was between John Cleese and Michael Palin; and Malcolm Muggeridge and the Bishop of Southwark, and can be watched here. I'm wondering how much of an effect it really had on the public view of establishment religion at the time. I really note how much less religion seems to matter in Britain compared to, say, America; despite the former being in theory a much more religious country than the latter, and I'm particularly wondering if this disparity can in part be attributed to this interview.
You might be interested in this older answer by /u/yodatsracist, which outlines the current major theories in scholarship for why Western Europe as a whole (not just England) is less religious than the U.S. as a whole. As you might imagine, what these arguments have in common is that they are structural, and seek to accommodate the exceptions as well as the major cases; also, they consider that the decline of religious fervor is not happening in the vacuum of one country.
Which is to say: in the context of that post, it would be argued that the above interview seen by a minority of the population of one country is evidence of the change occurring, and perhaps good publicity for it, not the cause of that change.