All of them, it's still pretty popular today. http://en.wikipedia.org/wiki/Journey_into_Space And still gets run on the radio http://www.bbc.co.uk/programmes/b00clkyv Some modern episodes have been commissioned over the last few years but they are not as good as the originals.
To be very pedantic, the first season of JiS is missing, bar one episode, but it was remade in a slightly shortened version a few years later, and that version's complete. Well worth hearing, particularly the ultra-creepy Red Planet and the early X-Files-ish episodes of The World in Peril (the last BBC radio programme to out-rate TV). The quick summary goes: Journey into Space (A Story of The Future) - 18 episodes, 1953-54, remade in 1957 as Operation Luna - 13 episodes (the remake omits eps 1-4 of the original, and condenses the original eps 12 and 13 into one episode). The Red Planet - 20 episodes, 1954-55 The World iN Peril - 20 episodes, 1955-56 The Return from Mars - 90 mins, 1982 Space Force (semi-sequel, originally intended as a continuation with the same characters) - 6 episodes, 1982 Space Force II - 6 episodes, 1984 Frozen in Time - 60 mins, 2006-ish The HOst - 60 mins, 2009-ish Oh, and ISIRTA is well worth a listen, particularly for Doctor Why and The Thing, and Professor Prune and the Electric Time Trousers!
I knew that but Operation Luna doesn't feel incomplete when you listen to it. Also worth listening to is the audio book of the novelisation of Journey into Space. It has what must have been covered in the lost episodes 1-4 and the reader does a pretty good impression of all 4 original cast members.
My copies of series six - the Time Trousers season - are a bit rough (do you know if there are any better copies in existence?), but it'll be a while before I reach them. Just finished the Cambridge Circus pilot and part way through the first 'prep show'.
I thought a bit about the palimpsest reconsturction you suggest. I can think of various technical reasons why there might be some reconstructable data left. Different aligment / missallignment of the tape / heads during wiping could have left traces, or how about magnetic traces spilling through on the back of the tape? And of course, work processes aren´t always followed to the letter. Maybe some reals where just recorded over without prior wiping accendently? If the new recording was shorter then the old, then at least a few scenes might still be left.