I am afraid the answer if he can come to UK or not depends on the britisch rules for the family reunion. As an asylum seeker in Germany, rejected or not, he has a possibility to go to a britisch embassy and make an application for a visum with the aim of family reunion. You must check before, what documents he needs or what conditions he must fulfil. He doesn't apply from his own country of origin and it is possible that the britisch embassy only takes applications from people with a residence permit in another country. In this case he really has no possibility from Germany if he has only his paper as an asylum seeker.
In most cases you can find the conditions on the websites of embassies or contact them through a mail although I have no idea if they answer soon.
If your husband fulfils all other britisch conditions for family reunion, it can be even better to make an application from his country of origin. And if he doesn't fulfil them all, it wouldn't be possible from any country.