Starting with TVP1, as posted by dbl earlier:
Easy to see how this could be adapted to the BBC logo for BBC1, but it is rather bland IMO.
Now, a thread like this has to mention the SF1 idents from about a decade ago - just superb, and would be on brand for BBC1. Actually see something like this working for C4 though with the blocks flying through the street.
The update wasn't quite as good IMO, but still decent enough.
And if you're looking for a "one" rather than "1" just looking across the Irish sea is a good start:
Red seems a popular colour scheme for the first channel. Any other examples to share - trying to concentrate on branding that incorporates the 1/one into the ident or graphics, rather than just slaps it on screen.