This is a strange point worth repeating. Textbooks like Samuelson contrast the market economies like the US with the state-run economies like the Soviet bloc at the time. What's stated is that the UK is half way between the two. Stated in a strangely blatent and serious way for such a misleading point. I googled
"cold war economics teaching" to see whether this has changed now, and
the first link that came-up suggests not; words like
"social insurance" or
"Social Democratic Party" would not fit the definition
"Socialism is an economic system that features public (government) ownership and production of goods and services".
The scan here is from my 1984 Begg textbook, written by a teacher at Oxford Uni where they have another short course in Economics, as part of the PPE degree done by so many wannabe politicians from David Cameron to Ed Balls. They both probably stared at exactly the same diagram. A few even went to ordinary colleges like Keele where Claire Short and Priti Patel studied, and looked at the same diagram or something just as misleading.
There are no numbers next to the diagram, but if you take it as a measure of the percentage of GDP controlled by the state - say 50% in the UK at the time - then the picture has a false simplicity to it. Since the 1980s, much more work is contracted-out but public-funded. So still public sector in a way. Other bits are more regulated, like banking, but still private sector in a way. When I started at Keele, National Express Coaches was used to a monopoly on long routes given in hope that they would return the favour by running short routes as some kind of back-room deal. I'd bought tickets on a rival - the tiny Stagecoach service from London to Scotland - but they were small and new and obviously private. Later-on, the roles were reversed. Stagecoach had a skill at predatory under-pricing that far out-gunned the ability of rival bus commpanies or the monopolies and mergers commission, so they could just take-over a 'hood like gangsters. They were specially interested in bus companies that owned valuable bus stations, to be sold after take-over. In a way, the monopoly power transferred to them and they became something a bit like the public sector in the sense of being the establishment or the big organisation with unfair power.
There are other services, called public sector on the statistics, that would have to be re-invented if the public sector didn't so them like compulsory insurance for sickness and unemployment. Every special case bamboozles everyone who isn't much intersted in it, and those who study the subject are not helped by the diagram above,
If you have a look at .gov.uk and the names of the ministries, it's clear that UK government is a kind of big insurance company providing services that we might use at some points in our lives but not at others. There was no ministry of economic command. There was no slice in the spending pie-chart for
"propping-up three million pointless jobs in nationalised industries to close in the early 80s". There is no Ministry of Economic Command to spend that budget. Simply not.