sorry, I misunderstood you initially, but now I understand that you want to display a fixed time, but in the users' time zone (and in 24 hour format) and that the time you specify is specified with London's timezone (UTC+0) – correct? What about daylight savings time?
For example, a simple solution using nothing but moment.js would be this: http://jsfiddle.net/wJGvb/
However, the output differs from the script you are using right now (for me, at least), by one hour because of daylight savings time.
I'm not too knowledgable when it come to time zones and all the little details and quirks, and then adding all the browser quirks on top of it. So maybe someone else can join in.