I am going to buy my first laptop, I already have a PC. My budget is around £350 GBP and I want one with a reasonable amount of RAM. I don't plan to use it for gaming. I also want an optical drive, a built in camera and mike & an HDMI output plus a minimum of 3 USB ports. Screen quality (brightness) is very important Ideally I would prefer one that has more than 1 years warranty that is valid in the UK.
So, my question is : Which ones should I consider?

For the price range, would suggest toshiba as some of the models in that price range have what you are looking for

3gb ram, built in camera, 3 usb port and 15.9" screen
-Now you would have to do some research for ones that have the HDMI port

That would be my suggestion for the price range and they normally would come with 1 yr factory warranty but always suggest to get an additional yr or two extended

Sorry, I couldn't figure out exactly how to use BestBuy.co.uk, so I used the .com version. (It seems the UK one is just a bunch of articles)

3GB|15" - 16"|Less than $600 : Laptop Computers - BestBuy

That will give you a list of laptops under $600usd (£377) with a 15" to 16" screen, 3GB RAM.

I would also recommend Toshiba.
Toshiba|3GB|15" - 16"|Less than $600 : Laptop Computers - BestBuy

I would imagine prices cannot vary too much from here (USA) to where ever you are (I'm guessing the UK). If so, this will give you a general retail value of the computer you're looking at. You'll have to go through the selection I sent you in order to narrow down everything else you want, but the model numbers will give you something to look at when you're shopping.

~Good Luck
P.S. Sorry if the prices are not accurate.