I think it's The Westminster Passion Play - Behold the Man (1951), certainly the dates are right. Furthermore, Campbell and Pitts note in "The Bible on Film" that "to evaluate the film critically would be unfair, as it was a church project and not meant to be a professional film", so this fits the "Bible Society" criterion very well.
On the downside, most Passion Plays wouldn't have much to do with John the Baptist. That said there is of course a chance that this one might have done. It was based on a play by "Walter Meyjes", but I can't seem to find that play for sale anywhere, so that can't be checked.
The other piece of info that doesn't quite fit is the Lady Leyes connection. There's simply no information on it that mentions her. This is far less critical than the above as lots of people would have been involved and I only have the name of the writers (Walter Meyjes and Walter Rilla), the director (Walter Rilla - pictured right), the producers (Susan Dallison and Fred T Swan), the narrator (Walter Meyjes) and the actor who played Jesus (Charles P. Carr).
Does anyone know anything about either the original query, or Behold the Man? I've not seen it, and wondered if anyone else might know more. It has never been released on DVD or video (as far as I am aware) though I would dearly love to see it. Sandra Brennan (All Movie Guide) notes that "This British drama is based on an annual production from Westminster Abbey and movingly chronicles the last days and subsequent death of Christ".
If you do know anything about the film in question please either post a comment, or email me via this form