Do a thought experiment. Imagine that the entire UK were walled in by an impenetrable barrier enclosing the country out to the boundary of its exclusive economic zone, and every record and memory of ownership were wiped away, such that no one could be entirely certain who owned what. Stimpson J. Cat pushed the History Eraser Button.
On the morning following the event, some boffins assemble and work out an emergency plan for re-establishing a workable economy, on the assumption that one existed before everyone forgot what it was.
Now, with no memory of the past, does the UK have the land, labor, and capital to completely provide for the needs of its people? If that costs £X per year, can the people of the UK produce £X of economic output per year, and with the correct proportions of goods and services?
(For your reference, the UK represents approximately 4% of the global economy.)
I reached my own conclusion as a result. It is completely workable mathematically. It just doesn't work within the existing legal tradition. That's the one that respects property and contracts--the one we all like because it's what we rely on to assure ourselves that the car we drove to work will still be there when we knock off for the day, and the house we go back to won't be full of grubby squatters when we get there.
But as much as we like it, those with more wealth, who lack the will or the imagination to spend what they earn--to keep the production-consumption economy circulating efficiently--like it more. It keeps the grubby middle class from building ugly-but-productive anthills and beehives within sight of their beautiful-but-inefficient homes, yachts, and luxury resorts. And that is what stops the socialist schemes to erase poverty--we just don't have the stones to commit armed robbery to do it. The middle class largely pays for itself, and no more, so the only available source for the necessary resources to haul the lower classes out of poverty is the rich, including the synthetic rich people better known as corporations.
So you swallow your lofty free-market, shalt-not-steal ideals, abandon your pipe dreams of one day being in the upper class, and you tax the rich at near-extortionate rates. Naturally, they would want to flee such a tax regime. Let them. Just stop them from taking the productive capital with them as they go.
It might work out like France. It might work out like Venezuela. It might work out like the USSR. But if it doesn't work out, it won't be because it is a mathematical impossibility. It will just be because someone made a wrong assumption in one of the thousands of possible places to make a mistake when trying to re-engineer an entire national economy.