Agree with what you are saying here. This isn’t the only track that is different to the album version. There are a couple of other Funtastik compilations that have longer edits to that of the album version. I can’t think of them off hand at the moment but there are a couple. By checking the compilation names and comparing running times on the original cd’s, there are edits. Presumably, these are done in house at the BBC. I would be surprised that the composers offered differing versions but I’d be happy to corrected on this matter. When I’m home and have more time I’ll get you the other examples of edited and extended tracks.
Also worth noting is FUN 1004 is a jingles cd and that track could appear on other later cd releases (although I've not seem them). On the cd; Reindeer Ride, there are 4 versions of that track with 30’ 10’ 59’ versions plus another ‘59 underscore version so suspect they have edited three tracks together making the longer version played on the Ceefax overnight pages. Having checked their re-released material under the Vibrant Music label, the same song only appears as the short tracks.
EDIT - Winter Chill on 'The First Noel' compilation has a run time of 05:43. The album run time is 02:59. On the same compilation and cd, 'The Fourth Reason' has a run time of 04:12 on the cd and the compilation runs for 05:03. Quite a few on those compilations show differing run times on the Ceefax compilations as to what is on the CD, so suspect that the librarian / compiler edits these tracks to extend the run times. To be fair, I hadn't given it too much thought until your post.
Christmas Glitterati which was used as a link track and also on the Christmas Tree compilation has a run time of 02:38 on the CD and the Christmas Tree compilation, but as a link track, it's edited to run a little over 6 minutes. There are plenty of others also that did this, not only on the Christmas compilations.