Just because 10% to 20% want to separate doesn't mean the majority do. Scotland was the last country to get a referendum on splitting from the UK. The people realised that if they split 100% they would soon go broke. So wisely decided to stay sucking the teet of the English. Now they would vote even more so to stay in the Union ever with the UK leaving the EU.
However. Countries want to rule themselves and the UK will leave the EU. Followed by a few more. Because there's no way the big German, French, Italien, Spanish car makers and other large manufacturers want to lose their biggest customers.
The UK can slowly replace the loss of the EU. The EU can't do the same with the world. It takes them 9 years to get a trade agreement and even then it's not that great.