So many things need to be overhauled, not cut as such. I would take a long hard look at how the relationship between public and privatised services really works.
I would look at ways for the state to both build and repossess homes and make a real effort to massively increase social housing, although I appreciate it would be very difficult to do. I would punitively tax second homes to support communities adversely affected and encourage second home owners to sell, and consider how to nudge people to downsize.
I’d look at ways to charge people a lot more for having massive cars.
Regulate the house building industries and enforce use of things like solar panels on new housing.
I would let the water companies fail, prosecute those who have run the companies into the ground and take them back into public ownership. Regulate the living daylights out of the railway companies.
Simplify the benefits system as much as humanly possible (almost a universal basic income scenario). Consider how some kind of nationalised jobs might work to support people to gain employment experience while doing something useful, instead of paying people to spend all their time either under stress looking for work or avoiding doing so. I would consider paying child maintenance directly as a benefit and taking it from the wages or benefits of the payer.
Consider how some jobs that are desperately needed but low status, like care workers, can have their status raised and how this could support others in society, and also how the state could support families to allow both parents to work if they are being held back by childcare costs. Look at ways to support women’s work and careers as longer term this will be good for society.
I would make it so that nobody got free prescriptions or bus travel but everyone pays a flat fee every time for the bus and everyone who’s currently eligible for free prescriptions pays a small fee like £2 or so. (I don’t think this would be very popular though).
Bring in dog licences and make them fairly expensive (not a vote winner either)
Look at ways to charge for some NHS treatment or adopt a kind of insurance system, but not with a view to actually covering costs - however I would consider publishing the costs of procedures and drugs so people understand these better. Look at how to balance salaries v benefits in the NHS and across the public sector, and how to retain experienced staff.
Put punitive taxes on food ingredients that have been proved to be either unequivocally unhealthy or environmentally damaging. This would be a token gesture to start with but should have a nudging effect and halt the downward spiral of cheaper and cheaper ingredients being used.
Sadly this would probably all cost money, at least to start with, but the very fact that ‘libraries’ is one of the first answers on the thread tells us there’s not much fat to trim!