Some Googling came up with this
"Liz ("4th. Dimension" series) Anthony Buckeridge 6 R4 4.5.1974 8.6.1974 Helen Worth/Jill Lidstone/Diana Bishop/Anthony Buckeridge " on a site listing lost radio plays - ironically it only came high up the sort order because I search for 'Anthony Buckeridge Fourth Dimension Angela' misremembering the name of the eponymous protagonist.
Anyway, now the BBC have put the Radio Times archive on line you can find the details here: http://genome.ch.bbc.co.uk/e74f3b408f94
A comedy serial play in six parts by ANTHONY BUCKERIDGE
Play produced and programme edited byGRAHAM GAULD
4.5 In My Opinion
ANN MOORE , ROLF HARRIS and TONY SOPER give their views on questions put by children of Witton Middle School, Droitwich, Malvernshire.
Producer ANTHONY SMITH
Ooh er, Rolf Harris.
Having put a name to the serial and finding that it is lost, is somehow rather sad. Though of course this was 1974 so maybe someone has a cassette somewhere. Not that I particularly want to listen to it again. It is more the nostalgia, small boys, Puffin Posts for goalposts, isn't it. Eh?
Anyway, Anthony Buckeridge's Wikipedia page didn't mention Liz. Until now.