Just to muddy the waters, Richard III was the Duke of Gloucester before he became King, so maybe Gloucester has a claim to his body too and he also lived in Chelsea, so London also has a claim.
I reckon Sir James Tyrell had a lot of the responsibility for Richard III's infamous reputation but then the poor devil was tortured. It is quite remarkable how many people Henry VII managed to silence one way or another quite early on in his reign. Now, he really was a nasty piece of work with absolutely no claim to the throne other than "right of conquest".