To help you and your team get to the bottom of the problems, they will have to be very specific about the issues that are causing them to be stressed.
I often find that people will generalise and say things like: "We are all stressed all the time, it will never work"
Essentially, you need to make everyone talk to you individually and to start their statements with "I" (not we, or some of us). Then make them specify what the problem is, how it makes them feel, and exactly when it occurs (and make them identify days of the week and times of the day, not just "during term times").
If you can help them to identify exactly what the problems are and you can get a list of statements like "Karen finds it very difficult on a Monday morning when she needs clear space to call 15 customers"; "Bob needs to have the same space on Tuesday afternoon and all day Wednesday to deal with the reconciliation files"; "Tracy gets cross when she arrives to use a desk and find that papers / cups / used tissues etc have been left there, and she has to tidy up before she can start work.
Then, you (and your team) can work out how to resolve the specific issues, and identify which times / days / situations cause real bottlenecks.
Then you can go to management with a list of specific requests that you need help with e.g. Strong, enforced policy on clear desks, access to 2 extra desks on Monday between 8.30am and 11.am, etc.
Good luck. It is a really, really tough thing to manage - removing someone's territory can makes them feel very vulnerable. But as others have said, some of these things which seem like idiotic cost cutting measures, are actually necessary to keep people in a job.