I'm just about to start ATC school in Spain I'm just about to start ATC school in Spain and so I'm no expert but I can give a European opinion. Yes, the UK accepts OTS applicants for their course but think of the size of the UK compared to the US, not only in terms of traffic but also in terms of population, the entire UK doesn't reach 50m people so there re considerably fewer applicants to screen than there would be in the States.
The UK accepts OTS applicants but as far as I'm aware they are pretty much the only Europeans to do so, certainly in Spain, where I'm going to school, you have to finance your own initial training, and I think the UK will go the same way in the not too distant future, there are already options to do this.
I recently saw a video detailing the amount of air traffic in the world and you really can't compare the situation in the US to anywhere else, you lot have much much more! The reason Eurocontrol has more controllers is probably because the European Single Sky is still not fully up and running and so there are still almost 30 countries to coordinate. Plus, with the possible exception of the New York area, we have a higher concentration of airports in general, so that's an added complication. And that's without considering trying to get all the Brits/French/Germans/Spaniards etc to agree with each other, never an easy task! In summary, you can't really compare the situations, they're totally different.
Whether or not it's worth trying to get in will have to be a personal choice, do you think you stand to lose more if you try and fail or if you never try?