The NHS. Effective regardless of critics.

The NHS as it is, albeit very costly, is very effective, regardless of critics.
It makes up a vast majority of our spending, and hospitals rarely stay within their budgets to meet standards. Costs have an increased with our ever rising population (which I'll go into another time), however it has definitely bridged the gap between rich and poor.

Those who are wealthy enough often opt for private healthcare (not free), however still pay taxes to fund those less well off. Not economically efficient, however certainly redistributes wealth on these Isles very well.

The downside?
What you pay for is what you get in life. Despite being a high quality service, getting that service to begin with is often troublesome. Operations can be set back many months, and unless you're in a critical state, you are very much at the bottom of the NHS's concerns.