No silver bullets + Baumol Cost Disease + greater expectations = very unlikely that services will become cheaper. Someone promising to make public services
much cheaper should be treated like someone offering to sell you a $10 Rolex. It's either fraud or theft. God help you if someone tries to sell you a computer system to improve public services, that needs
very careful management (18F, GDS,
not Capita and friends) if it's not to become a cost writeoff.
I should probably expand on Baumol Cost Disease: many public services inherently involve humans doing touchy-feely automation-resistant things, and as the rest of the economy becomes more automated or imported this gradually becomes relatively more expensive. Things like childcare, where the cost in childminder-hours-per-child is inherently fixed. You can raise the ratio (ie reduce quality), but you can't produce an hour of childminding in 50 minutes.
Besides, when redistribution is a goal in itself, it's a mistake to talk purely about cost and you have to look at outcomes.