I've now listened to the BBC programme by Roger Bolton here. The level of spin is pretty high, e.g. when we hear that the Shepherd of Hermas being 'dropped from the canon' (implying that it had a canonical status from which it could be dropped) and associating this with Constantine.
There is also a fascinating bit of editing, whereby the variant 'becoming angry' in Mark 1:41 is associated with Codex Sinaiticus (which of course doesn't have that reading). At 22 minutes 17 seconds into the recording we seem (at least from the intonation in David Parker's voice) to be breaking in midway through a sentence of his: '... in a codex Jesus is angry...'. The 'a' is almost sotto voce and the quotation continues discussing Mark 1:41. Then at 22 minutes 58 David is talking about 'the codex', meaning Sinaiticus. Since Roger Bolton's voice has interrupted between these two quotations one might suspect that a false join has been created between two quotations. Anyway, whatever happened Bolton has created the impression that it's Codex Sinaiticus 'the world's oldest Bible' which will shock Christians by revelations of an irascible Jesus.