My daughter is only 10 and we live in London but this summer I took her to Italy for a week to train in Civitaveccia and then to Barcelona. Both had good programs (Italians are super advanced on bar even at that age). Athletes are coming and going from all around Italy and the world to Civitaveccia. They even have a luggage room. Big, well equipped gym. Barcelona also has some good girls who have fed into the Olympic program in Madrid. I have contact both both coaches if needed. English wasn't a problem in Civitaveccia but it was all Spanish in Barcelona (my daughter speaks Spanish but I can't and needed one of the other mum's to translate). I would agree that the UK is hard to break into unless you have been elite from a young level; it seems over subscribed. I dont know how many times I've physically gone to gyms and left notes because I couldn't get a reply by email or on the phone... still ignored (eg Harrow/ Aylesbury). Heathrow and East London could be good options.