Welcome to the Wefugees community and thank you for your question.
Yes, it is possible for you to marry now. Since you are an asylum seeker, it's not possible for you to leave the country. Please read the following article from the Wefugees blog to get detailed information on how to marry in Germany (scroll down for the English version):
Regarding the procedure of moving to the UK with your future wife, please check out the following thread here on Wefugees and the links provided there:
Apart from that, I highly recommend that your girlfriend gets in touch with British authorities to evaluate the options you have.