I have had the opportunity to interact with several professional linguists and language trainers over the years. I have come to the conclusion that the most important thing needed to  speak like a native speaker is to stay amongst the native speakers of that language.

No school or training can give you an advantage in learning a language like staying and interacting with the natives does. I say this from experience of learning from the natives and being multilingual and fluent gives me a certain understanding of what I am saying.

Languages like English, Spanish, Arabic, French, etc. also have the distinction of being spoken in several parts of the world. That means that you don't really have to travel to UK to learn English the way I recommend. You can do so by being in the US, Canada, Australia, etc.

Obviously this is just one way of doing what you asked and I am pretty sure there are several more effective methods available.