Health insurance is irrelevant to the discussion in the UK so long as the NHS exists.

What is relevant is NI ("national insurance"), which pays for a bunch of unemployment and similar benefits: https://www.turn2us.org.uk/Benefit-guides/National-insurance...

What is also relevant is driver liability insurance - normally if you take paying passengers it invalidates your insurance, so commercial drivers either need to be insured by their company or pay more for correct insurance.

OK, but the idea is the same. You could have the big corporation pay the employed person X and the car insurance company Y. Or you could have the big company pay the self-employed person X+Y, and self-employed person pays the car insurance company Y.

If the big company is not willing to pay X+Y to the self-employed guy, they won't be willing to spend X+Y on an employee.

The only difference is if the big company can get better rates on the relevant goods than a self-employed guy.

If the self-employed person can’t afford their own insurance, but their employer doesn’t fund it for them, they often end up without insurance – and if they need to get something done anyway, society has to pick up the bill.

Self-employed people pay their NHS contributions the same way that companies pay for them. It's not a question of can/can't afford, it's a % of your earnings.

https://www.gov.uk/self-employed-national-insurance-rates

Apart from their not NHS contributions as National Insurance isn't a hypothecated tax

It's the closest there is to 'medical insurance paid by employer'. OR what do you think grandparent means when they say 'if the self-employed person can’t afford their own insurance, but their employer doesn’t fund it for them'?

The gig economy isn’t just an issue in the UK – the example I had used was Germany (which I had literally mentioned in my original comment), where exactly that is happening.