Immigration solicitor here. Some of the things people have said in this thread are wrong.
As an EEA national, you only have the right to live in the UK, as opposed to visit, if you're a qualified person or if you have permanent residence.
Qualified person means you're doing one of the following:
- working
- jobseeking
- studying
- self employment
- self sufficiency
Or you can be the family member of someone who is, so eg if your DH is an EEA national and he's working, you can legally be here as his dependant. But not if he's British or non-EEA.
There is a LOT of misinformation about this. people think you can just go and live anywhere in the EU you want and do whatever, but that's technically not true. In practice that is what the UK has allowed people to do, in many cases, but you don't have a right under EU law.
It doesn't actually matter whether you have a residency permit (not quite the right name, they're called registration certificates) or not. Those are just an admin thing. They're confirmation of a right you have. You could have one confirming you're a qualified person, they last 5 years, but you could have stopped being a qualified person despite having the documentation. This is all very poorly understood by the general public, and also the Home Office in fairness.
However, once a person has permanent residence, this all stops applying. You can come and go as you wish. You only lose permanent residence if you have been outside the UK for 2 years. If you come back in, even for one day, that restarts the clock. You need to find out if you acquired permanent residence when you last lived in the UK.
There is also the issue of being normally resident in the UK and thus entitled to the NHS. That doesn't have anything to do with nationality. A Brit who's just come back home after 5 years in Australia won't be, a Pole who's been here working for 12 months will. If you're not considered normally resident, you won't be stopped from receiving maternity care (they can't) but they can charge you for it.
You need to consult an immigration lawyer for advice on your position, and about how to make yourself a qualified person if you don't still have PR. The fact that you're pregnant doesn't mean you can't be one.
If you do have PR, any kid you have in the UK is British, but you might have some difficulty proving that. Sort it out sooner rather than later.