The majority of trade (imports, exports) the UK does, is with EU countries. You're very naive if you think the UK would be completely independent from the EU. It would be as independent as Switzerland -- which has lots and lots of biliateral treaties with the EU in order to keep the trade alive. Switzerland has to play by EU rules without having anything to say in Europe.
So yes, on paper the UK would be independent but in reality it would still have to play by EU rules -- with no influence at all. Yes, you'd no longer have to pay into the EU pot but also wouldn't receive any benefits at all.
This can work out -- but only if your island becomes a factory ground for foreign companies, from Asia to America, with rather low wages for the workers. Basically that is what it is already now because the UK has no own industry left worth to mention. Even the Dyson vacuum cleaners are being made in Malaysia. What you have, is a few brands and products that sell only within Britain, I'll grant you that. But if they're only being sold there, it probably means nobody wants them elsewhere or they're not competitive.
As I said: It can work out for you somehow but the majority of the British population will have to accept that they'll get poorer and that their money won't be worth much anymore. For instance, say goodbye to the Mediterranean beaches for holidays or to skiing in the Alps. That won't effect the rich upper class in Britain, though. I predict that difference between rich and poor will grow bigger, too.
And don't kid yourself with believing your old connection through your history of colonization will help you out much. With the exception of India, none of the markets in the Commonwealth countries can even start to compensate for the EU. And India can't be bothered with Britain anyway.
Basically Britain would be alone against the rest of the world -- like Switzerland. But Switzerland actually has a working economy and a working industrial backbone. Britain only has banks...
I really would like Britain to remain in the EU because I feel they belong with the rest of Europe. But if they decide they rather want to be left alone, so be it. Sad but all I could do was to shrug