There is much that you can research - I assume you live in or near the city.
This Forum has many threads that refer to industrial premises and factories that had their own defences such as pill boxes and even underground shelters and it is surprising what gems can arise in a thread where past reminisces are concerned. Make good use of the search facility - you may not get what you want first time so alter the wording and try again.
Following the loss of so much of the city's industrial heritage many of these structures have been demolished or erased but I am certain that records exist in the city's libraries of the city. Details of those such as the Lion Works (thread here on the Forum) are well documented as are certain WW2 artefacts at Longbridge Shadow factory and other large industrial places. Even department stores had provision for air raids. Some of these things still exist, such as anti aircraft gun emplacement structures in Sutton Park and Handsworth, a pill box at Lifford adjacent to the canal.
You might look into, if you haven't already, the working of the corporation: buses, trams, fire, ambulance, water, gas, electricity and the more difficult services such as rescue and removal of dead ans injured people. The water, gas and electricity supplies were a corporation affair at that time. I am sure the Police had much to do observing and policing much of this. For instance due to bombing of tram and bus garages many trams were stabled in the open further away from the city centre and major industrial premises. This proved a very successful move and I would not be surprised if the local bobbies were asked to keep a watchful eye on them.
I do recall policemen checking identity cards of people travelling on buses and trams. I do not know whether that was a regular occurrence or simply when looking for criminals, aliens or military deserters.
Much of this you already know probably, but hopefully there might be a comment or two which is helpful.