multiple visa complications

I may have one of the most complicated situations and need some advice. I am a US citizen currently trying to move to the UK, and have been in a long distance relationship with a British citizen for a few years.

I recently left my job to live in the UK on a visitor visa and just got back to the states. Hoping to return at the end of jan. We just found out we're pregnant, due at the end of Aug '11. Marriage is not an option for us at the moment. Is there any option for me to reenter the UK on a visa and have prenatal care?

If not, what effect will being born in the US have on the baby's citizenship?

If you re-enter the UK as a visitor any medical treatment will have to be paid for privately. Costs for the actual birth alone could be around £2,000. Also bear in mind that you can only spend 6 months in every 12 months as a visitor in the UK. If Border Control on entry believe you don't have a strong reason to return to the US and aren't entering as a genuine visitor you could be refused entry.
I believe that as the baby's father is British there should be the right for the child to claim British Nationality even though you're unmarried.