Applying for benefits can be an annoying task. I hope you get some help from this thread, and I always hope I can assist (please don’t take my words 100% gospel, things may have changed).
The reason why the DWP ask if your partner works is because if she earns enough then she can support you both, I know its ridiculous. It happened to my partners family, his father couldn’t claim JSA or any other benefit due to my partner working he has an income therefore he can support the family home.
You may be able to get around this by saying you don’t have a permanent address, in effect hoping home to home, and that her address is merely for mail purposes only. – Please don’t take my word for it in case I’m wrong. and claim for income-based JSA.
Hope this has helped 🙂