There are two who should definitely not be included and they are John Lennon and Princess Diana.
To include these two when leaving out such people as,
James Watt
George Stevenson
Sir Frank Whittle
John Constable
David Livingstone
The list is endless, before ever considering a pop star and a young woman that happened to marry the next in line to the throne.
It is interesting to note when thinking of great British persons, one tends to think of those in the past, but then I can't think of anyone alive today that comes anywhere close to these historic greats.