The UK does have employers NI contributions but that's not what I mean. The point is, if you spent a year to earn a gross £100k, and as you earn it, pay £50k of total tax, and with the remaining £40k/£50k you spend it on an employee at your company in salary and pay then £20k of tax, the government has that year earned £70k from that £100k passing through.

You can argue that really "£140k" has passed through, but it's not the case, because you created a new job that wouldn't otherwise have existed had you instead saved that £40k for a house. Either way HMRC gets £70k this year rather than £50k.

The wider point I was making is that all companies, even for-profit, pay tax to do just about anything, and companies with much lower sales than costs aren't just paying nothing. They generally have higher costs because they are paying people, and paying their taxes every month. The tax per employee is completely uncorrelated with the financial profit or thereof by the business, so it's a (sensible) misconception that companies that don't make profit like startups don't contribute to the economy. They do, by paying employment taxes.

I'm really making the point that you have to account for employee taxes (both employer and employee as you mention) for your costs as a business. That means, even though you already paid those yourself when you carried out the work to gain savings to invest in your business (to spend on an employee), you have to pay again when paying your employee.

I.e. Self-funded or businesses launched from previous accrued personal income where you invest your own time as well result in a bad tax situation;

whereas an employee earning £100k might pay £50k tax total and save £50k for a house (no VAT),

The alternate of investing that £50k in your business by paying someone £40k means you have to pay that employees PAYE, their Employer and Employee NI. So the government gets to re-tax most of that money when you use it to hire someone to build a new business with you, in a way they don't if you use it to buy a house, in terms of practical impact. When you pay yourself as an entrepreneur depends, there's dividends+PAYE in the UK (which requires yes you pay for both your employer and employee tax for yourself) or capital gains(ignoring tax schemes), either way, you do get taxed at some point to bring cash out.

The government in other words massively benefits from unprofitable for-profit companies so long as they hire some people, especially if the companies are self-funded. But even if it is investment, it's better to have that money spent on salaries now in new companies than sitting as stock in larger companies that keep cash reserves or use schemes to avoid tax. They get much more tax from people starting even unprofitable new businesses, than from employees who simply save money.

It's one of the reasons that since the introduction of income taxes (more or less WW1 in most countries!), you need money to get money in way that you fundamentally did not in the same way back when you could earn $50 from someone and directly use that same $50 to pay someone for the same skills without any loss of value.