There many online processing service online. Merchant Account is one of them it is a process in such a way that one can earn from his/her ecommerce site staying at your home. All the transactions through the ecommerce site are automatically performed through merchant account and it is possible for you to earn while you are in sleep. Merchant account is generally provided through the credit card companies like Mastercard, VISA, Paypal etc. But If you are thinking to have a merchant account owner you must be careful there are a lot of options waiting for you and there are some tips for selecting merchant account.

Do you know of a payment service for co.uk site??

Also what is the advantage of a payment gateway over Paypal??

It's not the domain extension that affects your ability to use a payment provider. It's your location. If you located in the UK then Paypal, 2checkout, and Worldpay are all options available to you. There are all third party processors.

Payment gateways aren't that important as they only act as online credit card terminals for your website. It's the true merchant account that they use that are important.

To compare true merchant account with payment gateways to third party processors, read this article. It explains it all in great detail.