If the baby is born in England, I'm pretty sure it would automatically have complete rights to everything in the UK. If this isn't the case though, the fact that the baby's father is English will make up for it. The baby will be absolutely fine to live and raise in the UK.
It can definitely have a British passport, because it's born in England and therefore considered British by birth. It depends on Finland whether the baby can have dual nationality and have a Finnish passport aswell. Many countries allow dual nationality, but many don't. My mother's country does not, so she lives in the UK and has doe for over 30 years, but she cannot have a British passport; even when she was married to a British man.
I@m pretty sure that if you moved to the UK when you were pregnant, they would take you in for antenatal checks as they do with everyone else. I moved away from the UK when I was pregnant, moved to Gibraltar (also British), and I was fully cared for, even though I didn't have paperwork saying I was local; I was still considered foreign, but they still looked after me and my baby.
I think you would get some form of child support, ot credits, but since I don't live in the UK anymore, I'm not sure who gets what, or what's available. But if you're with your partner, and he's English, he will automatically be entitled to support, so you should be included with that. In the UK, they won't let a baby go without. Especially if it's been born there and needs help, so even if your partner isn't entitled to anything, I think you woudl receive help if you needed it.
Have you asked him to find out? He could ask around and see what would happen, and put your mind at ease