We were in the same position as you before I joined and we had to go through hoops to get both LTP capital & revenue budgets (we had none). As Ian says if it is in the vicinity of any LTP funded schemes we try and get it upgraded at the same time, walking, cycling, safer routes to school, bus priority, traffic management act any thing that is in the LTP really. I suppose it depends where you sit within the council structure as well, we have taken everything traffic signal related into Engineering Services (including maintenance from Highways Maintenance) and we now work very closely with the team that implements the LTP
The other thing to do is to write a large report indicating which sites, how much money, impact if these should fail, statutory duty, claims against council and the new biggy if they don’t improve them to cope with TMA then they could be forced to do them all in one go! I think our bottom line was 3.5M deficit. This certainly made our elected members sit up.