Thank you for your question and welcome to our community!
As far as I can see, giving birth to your child in Germany will not influence your partner's case directly because you are not related to each other (from a legal point of view).
However, you are a British citizen which makes you a citizen of the European Union too (at least until further notice ;). You can try to get him a residence permit through that.
In Germany we got the following rule: If you come from a non-EU country, have a child with a EU citizen and you acknowledge partnity then you will receive a residence permit that enables you to live/work within the European Union. But I don't know if there is something similar in Great Britain and (if so) how it works in detail.
That's why I recommend you to get in contact with counselling centers in the UK since they are probably more competent about British law and the possibilities you have.
Apart from that you can also try to get married. Being married to a EU citizen will grant him a residence permit as well.