You can only qualify for automatic British (UK) citizenship if you were born in the UK or one or both of your parents were born in the UK. If this is not the case, then you will need to live in the UK for a few years and fulfill certain personal and residential requirements before you will be eligible.
As you were born in Germany, you may already be eligible for German citizenship and since Germany is part of the EEA (
European Economic Area), as long as you have/can apply for a German passport, you are free to live and work in the UK (or any other country that is part of the EEA) without needing a visa, which cuts out a lot of the difficulties that non-EEA nationals have when trying to move to the UK.
As the link posted above mentions (under Eligibility), EEA nationals living in the UK can get permanent residence after 5 years of living in the UK and then 12 months after they have gained permanent residence, they can apply for UK citizenship (providing they meet the personal and residential requirements).
If you were to go down this route with the idea of eventually gaining UK citizenship, you would likely then hold triple citizenship (UK-US-German) as you are already a dual US-German national (providing this is allowed by the UK, US and Germany). There should be no need for you to give up your US citizenship at all.