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Perhaps, I assume it depends on the country and your contract?
I invoice Sweden in GBP regularly and the company that pays me pays VAT at 25% in Sweden, but I have to zero-rate my invoice to them (B2B) and then need to document zero-rated VAT in the UK as otherwise HMRC would default to requesting VAT at 20%.
If the situation was reversed then I believe the Swedish company would zero-rate their invoice to me and my company would be 'Reverse Charged' as the buyer of foreign services and would then have a 20% VAT liability in the UK which could not be recovered.
I may have gotten something wrong, but this is my current understanding!
I imagine the NL company would expect an invoice without VAT? You'd then zero-rate your income within your Ltd company too (so would pay HMRC £0 VAT each quarter).
Otherwise, yep, simple cross-border engagement... you could choose to keep the business income in EUR, or GBP. Personally, I'd invoice in GBP because it's less hassle for your accountant (FX reporting).