That is great news. Anything from that era is bound to be classic folk. From our research these are the songs by Anne Briggs on the LFSC transcription discs:

LFSC Prog. No.        Performer        Title        BBC T-Discs        (P) Date

LFSC 01        Anne Briggs        The Recruited Collier        115618/115619        1966.4
LFSC 16        Anne Briggs        A Bower In My Breast        116855/116856        1966.12
LFSC 16        Anne Briggs        Polly Vaughan        116855/116856        1966.12

But I would opine that Peter Kennedy didn't record these per se - LFSC was recorded by the BBC 'live' at C#H. The recordings were then edited onto to transcription discs for the BBC Transcription Service, and clips were also edited for CFOF for the World Service.

It is likely that the Anne Briggs recordings - like the Sandy Denny recordings - have come from the original transcription discs of LFSC.