I've said YANBU but in a way you are and you aren't. I don't think asking the question or looking into your options is unreasonable at all.
A lot of NHS services vary by place in the UK, which means some people have vastly different experiences to others. FWIW, my experience in the UK and abroad is as follows (bear in mind I don't give birth until I go in on Sunday to be induced):
My first pregnancy was in the North of England and the "care" I received was so bad I was traumatized and terrified of ever getting pregnant again. The baby did not live and I nearly died too. I was so scared that I couldn't contemplate EVER getting pregnant again if it meant being pregnant under the NHS because at the time, I really thought it was an NHS-wide issue. I looked into private care and (at the time, IDK if it's changed) there was nothing fully private in the north, and going to London, the accommodation costs alone of being there pre-birth was actually more expensive than going abroad. Anyway, it was also the antenatal care that I needed to be better.
We emigrated to east Asia (for hubby's work) two years ago and my experience with this pregnancy was totally different. They had me booked in for a C-section from week 12. With my first pregnancy, I was convinced I was going to die if I gave birth because I just didn't trust the NHS maternity services where I lived and with my current pregnancy, I felt differently. At first.
BUT as this pregnancy progressed, I felt like the doctors (there were no midwives in the country I was living in this time around) wanted to do more and more unnecessary and invasive tests (all chargeable, of course). Literally none of my questions were ever answered and add into that a bunch of crazy cultural superstitions that the doctors believed even in this private, "western" hospital. The hospital was 2 hours' drive away and I got fed up by week 24 of them trying to call me in for stupid reasons, just to test more and charge us more money. When I (feeling braver by this point) asked if I could try for a vaginal birth I was told no for some made up medical reason that was frankly bollocks. I also got very fed up of getting ultrasound scans at EVERY appointment but not being allowed to find out the gender or getting/being allowed to take any pics to give to MIL etc. One huge issue was that we were paying for the hospital's translator and she literally couldn't be bothered to actually translate 95% of what was going on.
When I had some perspective on the whole situation, I flew back to the UK, but I was still determined I wasn't giving birth in the place I'd previously been pregnant. I just couldn't. So I rented a house in Northern Ireland (FWIW my family are Irish so that was also an option for us). Now, there are a LOT of stories about how Northern Ireland has the VERY worst healthcare, but actually they do maternity really well, and my care since week 34 when I finally got a house rented and got my referrals... I've been blown away. I'm booked into a wonderful hospital, with doctors and midwives I trust, I've seen the same doctor for my last 2 appointments and I have a named midwife who can answer my stupidest questions, and who will be doing home visits (OMG WOW) after the baby is born. I've met my HV already and everyone is just so supportive and helpful, without being interfering or telling me what to do. They ask my consent before doing simple things (had a membrane sweep 2 days ago, couldn't believe they asked before doing it).
I've learned there are places in the UK where you can have a baby that are fab and places that are terrible. And there are places abroad that are likewise great or awful. Only you can decide what is best for you. I strongly feel that we're in exactly the right place to have this baby. If we weren't getting such amazing care with this baby, I would have hired a private midwife or doula to advocate for me and prob had a homebirth so I would feel more in control.
And as a LOT of PPs have pointed out, please PLEASE think about neonatal care because paying for the birth is just the beginning. www.bbc.com/news/uk-england-nottinghamshire-47541801
ALSO think about the visa/passport situation. You don't currently need a visa for the EU, of course, but you will need time to get the baby a passport before you can come home and that's not always as quick as it should be, so factor in more accommodation costs for that. One of my friends got stranded abroad for 5 months because of a technicality and then a bunch of delays at the passport office after her baby was born overseas.
Sorry this was long but your question really resonated and I hope this helps.