The three 'seaxes' are the badge of Essex and in white on red would indicate Essex County Division.
The county divisions were raised in 1941 for home defence. According to Howard Cole's book, those in coastal areas were generally disbanded late in 1941 and replaced by Field Force Formations.
I'd suspect that a previous owner wanted to display his allegiance to his home county (or maybe he was just trying to pull an Essex girl ? )
I suspect that the 'Arm of Service' marking of '113' on black is the result of confusion. The white bar above indicates 'Corps Troops' and the black background normally an HQ function in which case it would have been displayed with a corps formation sign and not that of a division...
I can find a reference to '113' in the 1940 listings for an infantry division within an independent infantry brigade but then on a red background...223 Ind. Inf. Bde used the Essex badge also but with blue seaxes...and they wouldn't have been corps troops either....
Chris, If you're not a member on the HMVF forum then I'd suggest posting there with as much detail as possible re chassis numbers etc. and details from any data plates. It may just be that someone has researched the same contract.
As far as I'm aware, there are no surviving Morris-Commercial production records and no easy link with census numbers.
There are likely to be contract receipt cards with the Tank Museum at Bovington (with varying levels of detail).