Few years ago the EU adopted a manditory api standard for all of its banks. This, together with the lack of really big big banks and payment providers on the market, might've helped with opening the space to newcomers.
I’ll take a somewhat contrarian view to the other comments. There’s definitely a great deal of room for payment service providers outside the US so I don’t mean to discredit Payhawk’s success (I know nothing about them — they could be wonderful with a long life ahead) but Europe is going through somewhat of a FinTech bubble, a lot of these companies have very shaky futures when capital dries up. I don’t know if it’s a consequence of Stripe’s success, cryptocurrency induced finance obsession, the low barrier to entry… or a combination, but it’s a very frothy market here.
I see a lot of local effort in FinTech and in Health/MedTech. I think it's because both markets usually have a massive amount of local (i.e. national) legislation and bureaucratic red tape, making international solutions less applicable than solutions from the local market.
I actually expect to see the same happening with cloud services. Don't be surprised if Google, Amazon and Microsoft cloud services are driven out of the European market, because privacy laws make it illegal to host data on a Non-EU owned company (current rulings effectively already mean this, we are just short of really enforcing it. c.f. Schrems II).
For what it's worth, Romania's (UiPath) was not, they were a UI automation company. It doesn't detract from the pattern, but it does show it's not the only thing that has worked.