Lots of generalisations here, saying that "hospitals are filthy" is not true, though there are of course individual bad examples. The NHS has provided excellent care to many of my friends and family in both pregnancy/birth and critical illnesses. As has been alluded to here already though, having limited resources and being free at the point of use the NHS must focus it's efforts on the most important cases. Hence if you have a normal, no complication pregnancy you will be largely left to your own devices (you're not ill), but if there is high risk (premature, twins, etc) the degree of monitoring and care ramps up significantly.
I had a baby 2 weeks ago in Switzerland having had parallel prenatal care in both London and Zurich while I was still working and splitting my time between the 2 cities. The standard level of care, i.e. regular appointments and two scans for the key 12 and 20 week checks, are the same in both countries. If you get more than this in Switzerland you are either paying for more cover, got lucky, or had some medical reason why you needed more (and you would have got it in UK too). THe 10 days of midwife care in Switzerland is great but my midwife told me there are plans to scale that back due to increasing costs.
IMO you need to take responsibility for your own wellbeing and that means researching your options, asking questions, visiting hospitals, changing doctors or midwives if you're not happy, background reading, asking for help if you need it with breastfeeding etc, not just sitting back and expecting someone else to offer it.
I opted to have my baby at a midwife led centre in Switzerland, not a hospital, so i had all my check-ups with the midwives not with a doctor. With only basic insurance my accommodation afterwards was not paid for (it would have been in a public hospital) so we stayed only one night and then came home as we were happy to do so. In the UK I was given a choice of local hospitals or a home birth.
Also don't forget that good news is no news so whether you are reading the newspaper or surfing baby forums you will always be swamped with all the negative stories and hear very few positive experiences.
Btw you can fly much later in pregnancy than an earlier post suggested, depends on the airline, e.g. IIRC BA want a letter from doctor after 6 months and doesn't allow it after 36 weeks; Swiss only want a letter from doc after 36 weeks. Don't get them mixed up as I did once to my cost!