All fine, except you also have to stop free movement of goods across borders and/or put big tariffs onto imports, otherwise the UK firm paying more than firms in other countries goes bust because their products are too expensive and won't sell -- and then they have to sell all their product in the UK because the other countries will put up similar tariff barriers to protect their own industries. Which is also fine if the UK market is big enough to consume all their output, but most firms currently export a lot or product, so they then have to cut down production volumes and sack half their (now better-paid) workers. So there are new fewer jobs available so the out-of-work ones have to be paid for by the state, which means putting up taxes.
All of which leads to an economy where wages (for those working) are higher but so are prices and taxes, and unemployment is higher. It's difficult to see how the working man or woman will benefit from this...
The only way that this all works (better-paid workers, low unemployment, profitable industries that don't go bust, effective health care that doesn't bankrupt people, good schools for all) with a small first-world country like the UK is to increase the education and skill levels of the workforce so they can get paid more for doing more highly-skilled jobs making more valuable products that people want to buy; it's impossible to compete against low-cost economies with low-skilled jobs. This is the Scandinavian/German model, which also involves people paying more in taxes on the understanding that taxes are the price of living in a civilised society.
Unfortunately the UK/US mentality of "tax is a bad thing, government spending equals waste, privatisation is best" runs directly counter to this way of running an economy.
I'm in favour of socialism (society taking care of its weaker/poorer members using tax paid for by its better-off ones -- like me...), but only if it results in a society that doesn't go bust. The "Red Robbo" mentality of "all that matters is the workers, screw the bosses and the company, give us lots more money for the same work" doesn't pass this test; it didn't work in the UK in the 1970s, and it would be even less likely to work now.
The biggest problem is the mentality of most of the well-off, who see tax avoidance as almost a duty ("I don't use the NHS/food banks/council houses/free schools, so why should I pay for the scroungers who do?") but still want to live in a "nice" country like the UK. If tax evasion/avoidance, non-domiciled status, inheritance tax, higher-rate pension tax relief, and many other loopholes only available to the rich were clamped down on, there'd be plenty of money in the coffers to pay for things like better schools, NHS, properly funded universal credit (if it was fixed!) and so on -- but given this mentality, any UK government trying this would first be bombarded with protests from the Express and Mail and Telegraph about "squeezing the rich", and then if they persisted many of said rich would move abroad to protect their wealth -- ignoring the fact that this wealth was in the end generated by the workers that they don't want to benefit from it.
If anyone can suggest a way to cut this Gordian knot in a way that doesn't result in businesses and the country going bankrupt as we roll back to the 1970s, I'd love to hear it...