When I co-founded a company in the UK in 1995 there were two £1 shares - one for each founder. Mind you it was an off the shelf company - but the process couldn't really be much simpler back then - and its probably a lot simpler now.
You can open an Estonian company with 0.01 € capital. It will look ridiculous in the registry, and you will still be liable for the remaining 2499.99 € personally anyway, but it is possible. I’ve seen a couple 100 € companies, which is more reasonable I guess.
You can also declare that you’ve paid the capital in, without any proof required for small amounts (up to 50k € IIRC). If you lie about it, I suppose you’ll be personally liable for everything, so definitely not worth risking it. Just put in like 500 €, set it aside on the business account, and don’t touch it.
(IANAL)
For a limited company in the UK, you need a number of pieces of legal paperwork which I think you can technically write yourself but may prefer a solicitor to draft them correctly for you, and then you pay £100 to register the company, and you (and any other directors, shareholders or guarantors) capitalise the company yourself.
You are now limited in liability for what the company does, to no more than the capital you put into it.
You then have to supply yearly accounts, may have to register for corporation tax, VAT, register as an employer for paying national insurance, you'll probably need business insurance, etc.
https://www.gov.uk/set-up-limited-company