According to Kal'95...
Special: 16-9-60 - Junked
Series 1: 26-4-61 to 31-5-61 (6 eps) - Episode 1 exists
Series 2: 5-10-61 to 9-11-61 (6 eps) - Episodes 5-6 exist
Series 3: 19-4-62 to 31-5-62 (7 eps) - All bar episode 4 exist, including unused film inserts for episode 7
Series 4: 4-10-62 to 8-11-62 (6 eps) - All exist
Special: 19-4-63 (Montreux entry) - Exists
Series 5: 3-5-63 to 21-6-63 (8 eps) - All exist
Series 6: 14-11-63 to 31-12-63 (8 eps) - All exist
Series 7: 27-9-64 to 20-12-64 (13 eps) - All exist
(Kal lists them all surviving on 35mm, which is apparently not correct - some are on 16mm.)
The revival edition ('Michael Bentine's Square World') from 19-4-77 also exists...
"I can honestly say that I've received thousands of letters since I last presented this program in 1963. But in spite of them all, here is another edition of It's A Square World!"