I am a teenager living in the UK and I want to buy an electronic device to do this on:

Browse the internet.
Stream music.
Use Deezer (deezer.com).
Check emails.
Manage files (which I can't do on a smartphone, smoothy!)
Shop online.

I want to do this for as cheap as possible, so what should I get and where should I get it?

Also, I don't mind people outside of the UK answering this, but they probably won't know where to buy it from in the UK. Any help is greatly appreciated though!

How are you going to shop online since that requires credit cards in most cases... and as a teenage how are you getting a credit card.

As far as the rest... any smart phone will do what you want. Consider them a small computer that fits in your pocket that also works as a phone.

Any place that sells Cell phones will sell them. Which is almost everywhere.

And like everything else... there is cheap... and there is good. There isn't cheap and good.

You have to decide how much you are willing to give up and how much you are willing to spend. And find a balance you can live with. Meaning if you want a Samsung Galaxy or an Iphone... its going to cost you a LOT of money.