Giraffe...there is a huge reluctance amongst men to go to Doctors or hospitals. Admitting you're ill is like admitting you are weak to them. You'll also rarely see a Traveller wearing glasses as they class poor eyesight as a failing.
Women are usually fine about accessing healthcare but the lifestyle of some can make it very difficult. If nomadic, it's difficult to get registered/stay registered with a GP. Hence, they are big users of acute (a&e) services because that can often be the only way they can see a doctor. Consequently, their medical history can have big gaps in it, deoending on the level of sevices they have been able to access.
Pregnancy care is better these days as a huge amount of work has been done to educate about the importance of ante natal care. The last official stastics that I am aware of were that infant mortality was about 10 times higher in Traveller population than in the general population but I expect that might be a bit lower now, or in the near future (hopefully...as that figure is horrific in this day and age).
Uptake of childhood vaccinations has also increased massively (almost 100% in my area, up from less than 50% a few years ago, due to the work of some very dedicated HVs).