I sympathise with local councils who are having to find substantial savings, though I suspect there are many councils where the savings are much easier to find than others!
I struggle to believe any expenditure by government (of any party) is as efficient as it would be in the private sector. One brief example; I know of one local council which spends £5.99+ VAT for a ream of photocopier paper, when I buy exactly the same brand of paper for the West Kent Office for £2.75. When I asked why, no-one knew. After a bit of digging and a FOI request it transpired that the Council in question used a procurement company for their stationery, who obviously added on their own fees and handling charges, resulting in a doubling of costs. I suspect many councils do likewise. £3.24 extra on a ream of paper may not seem significant in itself, but over 5,000 reams a year it equates to £16,200 of additional expenditure.
The issue, however, isn't the cost of paper - it's the whole process of procurement and best value. It is reasonable to assume that if a council is spending over twice what it should be spending on photocopier paper, it is probably spending twice what it should on envelopes, paperclips, office furniture and pens and post-it notes too.
It is probably unfair to blame local councillors for this. They are elected to set policy and direction. Having instructed their Officers to buy the cheapest possible paper, they should have confidence in that decision been implemented. I suspect what would happen is the relevant officer would say to the procurement company "we want the cheapest possible paper you sell" without actually checking if that product could actually be sourced cheaper somewhere else. This is a real example of the dangers we face when those who spend the money don't have to pay the bills!