It's certainly chrome, but in the BBC's defense that particular clock has a special place in the hearts of its viewers. It's the one that used to be used in the run up to "Programmes for Schools" broadcasts and is therefore very familiar to everyone of a certain age.

There's also the fact that the BBC is a broadcaster with schedules, so while you might not care if you know the time, the BBC wants you to know it so that you don't miss broadcasts.

For these reasons I think it's superfluous but in-offensive.