How do I invest in an index fund in EU? (or UK)

The main thing you need to know about index funds is that 4% annually is a long-term average, and the actual annual return will fluctuate wildly. It could be -20% one year and +30% the next year. If you can’t stand to lose 20% or more of your savings in a year, then look at something safer (but which will therefore have a lower average annual return).

If you’re comfortable with the risk, just open an account with a reputable online broker and choose an index fund from the ones that they offer. In the UK they’re generally called investment platforms or fund supermarkets, so you should search for those terms — there’s a good introductory guide here. If you’re resident in the UK for tax purposes, it will make your life simpler if you use a UK broker.

Dividends and capital gains are taxable, but in the UK the first £2,000 of dividends and the first £12,300 of capital gains each tax year are tax-free, so on a €70,000 investment you can probably avoid tax almost entirely by selling enough each year to use that year’s capital gains allowance and then re-investing (but you have to wait 30 days before re-investing in the same fund). You can also put up to £20,000 per year in a tax-free wrapper called an ISA.