Why do websites ask me to accept cookies?

Under the UK data protection laws, websites need your consent before they are allowed to set any cookies other than Essential Cookies and should always give the option to refuse Non-Essential Cookies. Some websites go further than this and give you the option to decline all cookies.

Option to refuse Non-Essential Cookies – if you refuse Non-Essential Cookies, you might simply not experience the full functionality of the website as it won’t have the ability to recognise you or provide a personalised experience. However, you should still be able to access and use its main features.
Option to refuse all cookies – if you refuse all cookies, the website you have visited may not function properly due to you having refused Essential Cookies as well as Non-Essential Cookies.