Earlier quoted context omitted.
I love Bagpus. There's also Mister Ben (not sure this stands the test of time) and Ivor the Engine. (And I have fond memories of Danger Mouse, but I'm not sure that's any good either).
Well, you can't go wrong with Oliver Postgate, who I now notice made nearly half of the programs in my (completely randomly selected) list... Also I appear to have remembered a fairly small selection of the 'children's television on drugs' genre. See also: Banamaman, Jamie and the Magic Torch, Roobarb and Custard, Captain Pugwash... While talking about children's television: it's not British, and it's slightly later,…
It was co-produced by a British television company (TVS), and had specifically filmed inserts that replaced the Inventor with a Lighthouse owner (the sequences were arguably better too, certainly less rambling and more focused).
But even if you ignore the inserts (others were filmed worldwide) it's still partially British