The UK does not issue Dispatcher Licenses. They simply file a waiver of the requirement to have it's people have Flight Operations Officer (Dispatcher) ratings with ICAO.
This is because is is a sure fire way to keep people from unionizing in a volitile industry such as as aviation.
What you can do, if you are a Jeppesen graduate or industry experienced enough, is go to the U.S. and take a short course to get your ICAO FAA certification that is well recognized and considered the world standard all over... after all it was the U.S. that created the rating almost 80 years ago in the first place.
Either way, some experience will go a long way well beyond the EK College Jeppesen FAA course that is technically not an FAA course outside the U.S. and you should never be entitled to credit for such unaudited training to be able to take a short course in the U.S. but somehow the Denver FAA FSDO looks the other way for Jeppesen... so good luck and go for it, if you can get the visa to the states and afford it too.
Good luck!