Top level .UK domains are a recently launched namespace and as a result many generic and valuable domains are still available to register. However Nominet, who are .UK governing body, has restricted the registration of top level .UK domains until 2018. They can still be registered but only if there's no existing second level .UK domain (.CO.UK, .ORG.UK etc) that was registered before the 10th June 2014. If there is then only the owner of the second level .UK domain can register the Top level .UK domain.

Example 1:
You want to register houseandhome.uk and it is shown as available but houseandhome.co.uk was registered in 1998. As a result you'll be unable to register houseandhome.uk unless you're the owner of houseandhome.co.uk.

Example 2:
You want to register houseplushome.uk and it is shown as available. Houseplushome.co.uk is also shown as available so you should have no trouble registering houseplushome.uk.
The rule of thumb for accurate .UK domain registrations is to use the default search options and search for all possible United Kingdom domains. If all domains ending in .UK show as available then you'll have no issues registering the top level .UK.