There were/are several in exactly that situation working for at least on UK airline so hopefully one of them might spot your post and give you a definitive answer.
In the meantime, as a starter:
As Banana Joe says the important thing is the bi-lateral tax agreement between the NL/UK..but speaking as somebody who worked UK but lived elsewhere in the EU how it
can work is:
If in the UK <90 days then the UK assess you for income tax based on the proportion of your total duty time spent in the UK and UK airspace..
The country of your residence may also assess you on your global total income and tax you on that,
minus the tax you've paid the uk ( but see the bi-lateral).
As I have been told I can not get health care insurance in the Netherlands. It is a mess!
If working in the UK you may well pay "National Insurance" (NI), roughly speaking equivalent to "social charges.." As lear999wa mentions pre-Brexit that would probably entitle you to healthcare in your country of residence in the EU, I have no idea where that stands at the moment. If you
are already in the UK and paying NI you need to talk to the non-residents section of HMRC about now it now works and the possibility of getting coverage in the NL using a "portable healthcare document, aka an S1", which is issued by HMRC.
Apologies for all the "mights/mays", hope you get a definitive answer soon.