Not exactly radio but this show was Broadcast by Rediffusion in 1964 the show hosted by Keith Fordys also had a co-hosted - Dusty Springfield.
The show included;
The Beatles - Twist and Shout
Dusty Springfield - Interview with George Harrison
The Animals - Baby Let Me Take You Home
Keith Fordys - Interview with Eric Burdon
Lulu - Shout
Keith Fordys - Interview with Lulu aged 15
The Rolling Stones - Not Fade Away
Millie Small - My Boy Lollipop
Dave, Dee, Dozy, Beaky, Mick and Tich - Glad all Over
The Four Seasons - Rag Doll
Gerry and The Pacemakers - Ferry Cross The Mersey
Keith Fordys - Paul McCartney judges mime competition to;
Brenda Lee - Let's Jump the Broomstick
Keith Fordys - Pail McCartney mime competition Result
(see video)
https://www.youtube.com/watch?v=IgQ1qNPciic&list=PLOADA5ONwYCY0gb1hxIuayMZkXDqd3r1s&index=8
Peter Cook and Dudley Moore - Goodbye
(see video)
https://www.youtube.com/watch?v=J5ya_Gq8d4Q