Good idea - I will check with an Immigration Lawyer next time we're back in the UK.
As a thread-drifting aside, re
"Try it with a relative's United States of Gordon Brown address?"
I regularly checked into Hotels around the world and put my address as
"Windsor House,
Buckingham Palace
London"
or "10 Downing Street, Westminster, London".
Childish of course, but it made me laugh.
I even did that on immigration forms - Thailand and Korea (South not North

) spring to mind.
Probably best not to try that entering the USA