This does happen in Finnish tax system. Your tax rate (percent with one decimal) is calculated based on your annual gross income. Rates are supposed to be calculated smoothly, and they are certainly calculated for each individual separately.
In reality they are step functions. It is surprisingly common to have people refuse promotions because if would put them above an income tax threshold, bump up their rate, and end up with less money after taxes in the end.
The UK tax system is far from fair but at least it has clear brackets: income above threshold X is taxed at rate Y.
Are you talking about this tax system? <https://nordisketax.net/pages/en-GB/taxation/?country=finlan...>
Because that is a marginal system, (and unless they've messed up the calculations, which they haven't in this case) you should never end up with less from earning more. Can you give an example of two income amounts where the lower income ends up with more money after-taxes than the higher income?
Or is it the additional municipal, church, or health levies mentioned on that page which have the discontinuities?
The UK system doesn't either though. The rate for 100-125k is higher than for 125k+ due to the phasing out of the personal allowance. It gets worse if you have kids and can even result in a >100% marginal rate.