Good point. (Pretty poor of me not to spot that when I live so close to
the River Lee which formed the boundary between Middlesex and Essex.)
Looks as if it the arms represented the areas which were (in part at
least) within the MBW area *or which bordered it*.

Annoying isn't it. BTW if you want a clearer image of the arms there is one
he

http://www.pbase.com/john_cooper/image/75644122/large

There is a castle sort of thing on the Hammersmith & Fulham coat of arms but
I've been unable to isolate what it represents.

G.