And on the last bit: I said in an earlier post that there are different routes to the same goal. I don't care what the reasoning is, as long as the goal is achieved.
Wait, but what is the goal? If you think all parties share the same goals with respect to social outcomes, you are mistaken.

Let me show you another picture from the supposedly neoliberal Blair government that you are so critical of. Under the Blair government, the health service (that you are so keen on in the US threads) and education received more funding in real terms than under any other government in my lifetime (a critical BBC summary of his era described these increases as huge). What matters more to you? The neoliberal label that your circle describes Blair as? Or the investment in public services that he realised? Do you disregard the latter because of the former? Actually, any objective assessment would see that the latter makes the former description a false claim. You can't be a neoliberal if you direct funding into public services as a primary goal.
What about compared to governments before Thatcher? What happened to the funding after Labour lost the government? What were long-term changes to funding or governance, and were they good or bad? In principle a neoliberal is perfectly capable of rolling out public funding in one area while restricting it in another. The destinations and conditions of funding also matter. For example, in the United States one popular neoliberal policy has been to fund "school choice" by redirecting parents from the public system to private schools and charters with subsidies and vouchers (i.e. government money for private industry).