There are several things involved:
Bigger issue, in my opinion, is showing exact time. Assuming their servers all keep exact time and that everybody is happy with their definition of the exact time (which is a big assumption to begin with), BBC would also need to take into account latency between server and client. E.g. it takes about 1/3 or 1/4 of a second for me to load a single random page with a GET request from BBC.
For an example of pain it takes to give users correct time, visit The official U.S. Time page. It's a java applet, presumably because anything client-side can't be trusted to actually count a second as a second. Granted, that page is ancient, but you can still see that it's not really trivial.