My guess is that it was specially composed for the ident and isn't available elsewhere. That's what BBC usually do with their idents, much to everyone's dismay and would explain why it isn't easily recognisable from any other source.
It may well sound familiar from somewhere else but that also seems common to BBC idents too; I suspect it just sounds very much like the other tune you heard.
Could be wrong, but just going on past experience- as the BBC isn't a commercial enterprise it makes more sense to just specially commission their own music for these things.
BBC2 Ident music - can you identify it?
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