There would seem to be a lack of representation of
Surrey which might perhaps be a clue to where the remaining two arms
might be from.

Yes. And of Essex if it were the MBW.

It's been nagging at me so I've dug around a bit more.

I'm pretty sure that 1 o'clock is Guildford (the county town of Surrey).
I've not found details of them as they were when the bridge was
commissioned but the former Borough Council's arms were very similar and
incorporated a castle with 3 towers between 2 woolpacks. See
http://www.civicheraldry.co.uk/surrey_ob.html

5 o'clock seems similarly to be the county town of Essex - Colchester.
See http://www.civicheraldry.co.uk/east_anglia_essex.html

I can understand why they used Colchester's as the arms of Essex
duplicated Middlesex's. But I haven't been able to find a reason for
not using Surrey's (assuming there was such a thing).

--
R