For a European company or a business with a presence in european countries (including the UK or not) the .eu domain extension is suitable.
If you want to choose a domain name for an organization go for .org or .org.uk if it is specifically a United Kingdom organization.
If you want to choose a domain name for an individual or family website in the uk, you could choose a .me.uk or .name
The .info domain should be preferably used for information rather than commercial websites.
The .mobi domains are suitable for mobile websites.