The only death for a George KIRK in Kent in 1946 is:
George KIRK age 76 Jun 1946 Dartford v.2a p.929.
The age matches the year of birth you've given.
This George KIRK appears on the probate register as follows:
George KIRK of 19 Methuen Road Bexley Heath, Kent d.21 May 1946. Administration London 15 October to Margaret Kathleen Allen (wife of James Kingsley Allen) and Thomas Harry William Hitchens engineer. Effects £252 9s 1d.
There is a marriage in June 1933 West Ham of Margaret Kathleen KIRK to James Kingsley ALLEN so it looks as though this is the family you're looking for.
Obtaining the death certificate may provide additional clues, such as name and address of other relatives.