The W8 form states that you are not a US person and therefore you are not obliged to pay regular taxes every US citizen has to. However you may be in obligation to pay 30% income tax as an foreigner.
The companies based in the US usually requests W8 and W9 forms so they wouldn"t run into any problems with the IRS. Some companies like Shareasale CPA network
and Google only require you to fax them signed statement that you don"t have any connections with the USA (which you don"t if you operate as an affiliate only) instead of W8 forms. With this statement you are not in any obligation to pay any taxes to the US government as far as I know, nor will anyone require you to.
As for W8 form, if your country has a treaty with the US which prevents double taxes than you won"t have to pay 30% of your earnings to the US government. UK should have this treaty signed.
However if you live in a country that does not have this treaty with the US government, than you are in obligation to pay 30% of your earnings to the US government and usually the company you work with will automatically deduct 30% from your earnings.
Hope this helps!