To what extent is the university budget public?
The key to this information request would be the Freedom of Information Act. The act has lots of things which you cannot request information for, however. One of them is "trade secrets". I don't know if construction work can be considered a trade secret.

Timothy Gowers documented his attempt to get UK universities to reveal their journal subscription costs on his blog. This sounds relatively similar to what you're thinking of. If you attempt to get the same information, I'd guess you'll need to use the same methods, will meet the same obstacles, and get the same results (i.e. you'll eventually be successful).