One of your interviewees (I didn't catch her name) made a misleading statement. The government are not cutting £6bn this year, that was what they cut just before Whitsun. Total cuts this year are £60bn. The last cuts were just a taster.
Personally I agree with the other interviewee, now is a very very bad time for large cuts. Large cuts now are a recipe for disaster and a double dip recession. Small cuts are possible but we shouldn't be looking at large cuts this side of 2012. I'd look at cutting the JNC grades (very senior managers, mostly £100k+) in local government and equivalent in other bodies.
Interestingly, my suggestion of cutting senior managers is what Stephen Hughes (Chief Exec of Birmingham City Council) is apparently considering.
I also like the 'Total Place' proposal of the last government. Rationalise and link up public sector systems and bring them under a single management structure so the UK can leverage economies of scale to the greatest extent. Even something as simple as a single payroll system for the whole of the UK public sector would save incredible amounts and make enforcing equal pay legislation a breeze.