Anyone that says "free" anything needs to remember that the money has to come from somewhere. If you are willing to pay a lot more in tax then by all means that is your option.
We need to have a serious think about what the NHS can and cannot provide in the longer-term. The sheer volume of non-essential stuff the NHS has to pay for is actually astounding. I also think we need to cut the HUGE amount of red-tape the is engulfing the NHS if we are going to be efficient. This means cutting duplication, nonsense referral processes etc. For example, I had an A&E attendance some time back and needed a referral to a specialist. A specialist that was literally across the hall. I had to get a GP to refer me back into the service because they needed to commission it. It was ludicrous. Also they need to do ALOT more outreach to catch illnesses earlier - I would advocate health buses that pitch up at supermarkets and give free health checks, blood tests etc and can then advise on what to do next. Plus there needs to be a massive culture shift away from "NHS can fix me"...NO! You need to stop getting into a physical state and expect the taxpayer to foot the bill. Nobody seems to want to actually take responsibility anymore, no wonder the NHS is in the state its in!
I would also suggest fines for missed appointments is a must. If you have a phone you can contact the GP to cancel, there is simply no excuse for missing appointments without letting them know. Yes it may impact the poor more, but I am not in the business of fragilising the poor. We must take much more responsibility for our behaviours. I know someone who works in outpatients - she has to book in appointments in advance and can't just "slot in" patients if there are non-attenders. She - at one point - averaged at 23 HOURS of missed appointments PER MONTH! 23 HOURS! She couldn't be sent elsewhere because it is all prebooked up.
In other areas, child-care needs to be under public ownership - not for profit. So parents can pay a reasonable cost for the actual cost of the care being provided but any extra goes straight back into the service and/or reduction of fees. You could charge a household £500 a month for childcare because with 40 kids at one children's nursery what would more than pay the wages of the staff etc. Greedy owners have no place in care settings.
Outlaw multiple ownership of properties. If you own two that is your maximum. If you own 3,4,5, 10, 100 houses/flats then you have to sell them. It isn't okay that the market is run by a relatively small number of landlords who sit back making a profit off of hard working people. I don't mind someone owning a few properties but it is disgusting how there are no houses for poor renters yet millionaire landlords make a fortune.
Replication of what works across all state sector organisations. If one NHS trust is exceptional, then that learning must be shared. It isn't at the moment.
Prison services need serious reform. I would actually go so far as to say that any offenses for non-violent crimes need managing in the community. We need to use the talents of criminals to the public advantage. You could have supervised community service (with a probation worker) and still it would cost less than prison per person. For example, Boris Becker was a world champion tennis player. He spent time in prison. Surely we could have had him coaching in schools/colleges and giving his experience over to help the next generation? We need to get away from the idea that being a criminal means you can't do anything good for society. For those with no skills, put them out to work in a public facing capacity and make it blatantly obvious they have committed a crime. Wearing a yellow tabard with their name and offense on the back. Shame them into stopping. I'd go so far as to say that anyone that has a violent criminal background should be placed on a "name and shame" register online. Make crime so aversive that they stop it. At the moment, prison is too easy an option.
Just some thoughts.