‘.co.uk’ or ‘.uk’ mean much the same thing and they are ideal for any business or individual who is solely UK-based and really wants to let people know that they operate within the UK.
‘.org.uk’ is extension designed for ‘organisations’ – which can be a slight grey area when trying to figure out what exactly defines an ‘organisation’ – but for the purpose of domain extensions it simply means ‘non-profit organisations.’
In 2007 when I was looking for a domain name for another trust of which I was a member, ‘.org.co’ was not available but ‘.co.uk’ was and that fitted the bill for a number of years so when I joined the Northumbrian Fisheries Heritage Trust, nfht.co.uk was taken rather than the one for nfht.org.co, without much thought behind the choice being made.