Welcome to the Wefugees community and thank you for your question!
Marrying your partner who is an asylum-seeker in the UK should generally be possible. You would need to prepare two different steps: First, what you need to do as a German citizen in the UK in order to get married (also to make sure your marriage will be recognized by the German state), and second, what your partner as an asylum seeker in the UK needs to do.
I'm not an expert in either of these topics, but I've had a look and found a website explaining Marriage in the UK in general: https://www.gov.uk/marriages-civil-partnerships
And also: https://www.gov.uk/marriages-civil-partnerships/foreign-national
As I couldn't find a fitting source regarding asylum-seekers' rights to marry in the UK, it may be best to contact a refugee support service like the Refugee Council: https://www.refugeecouncil.org.uk/contact
They have more experience and can probably lead you in the right direction.
I hope this helps a bit. Feel free to share any more questions you have with us or update us if you found any helpful information!
All the best,