Edit: I just checked the headers that are sent along with any request to bbc.co.uk, and the response already includes the current datetime. So basically they don't even need to implement a time server anymore, but just do an Ajax request to document.location, and read the Date header on the result, to get the accurate time. They can just upscale their servers a bit to handle the extra requests (or implement an empty-response URL). Why would this take 100 days again?
Edit2: Sample code here: https://news.ycombinator.com/item?id=5825319