The 2 usual connections are:
close relatives (such as parents, children, brothers or sisters) already settled here
long, relatively recent periods of previous residence here
These factors may be taken into account as part of a close connection (although they do not show a close connection on their own):
longstanding ownership of substantial property in the UK
long periods of employment by the government of the UK or a British overseas territory
employment with a UK company involving frequent business trips to this country
past service to the UK resulting in the establishment of close contacts with this country
letters of support from eminent British citizens
British status that is not full British citizenship (such as British subject status, British overseas citizenship, British overseas territories citizenship, or British protected person status) is not considered a close connection with the UK.