Sunrise, I have been in this situation, I was told regardless of circumstances you have to be given emergency accomodation initially if you have a child, they will then look at the circumstances of you being homeless, if they decide you are intentionally homeless they do not have to legally provide you with permanent accomodation after this but they do have to emergency house you if you have a child initially.
If you have not paid your rent because you CANT there are different rules to if you WONT.
Be aware that if you go down the route of waiting out the tenancy end and making them take you to court to evict you that the council will wait till the very last minute until literally the day you have to be out before helping you.
If you do wait it out and make them take you to court you would be better going to court and speaking to the housing arrears advisors (they do set help days here) and explaining the situation, explaining YOU cannot pay and you would be better explaining your home situation to them as if it goes to court it will be in both your names as joint tenancy.
I do think it would be best YOU (not him) need to get out before the end of the tenancy, I certainly think.
If you ever want any practical help, someone to come with you to solicitors, appointments, somewhere to leave smaller stuff, an emergency place to crash the night etc I would be more than welcome to help!
FROM SHELTER
"If you became homeless because of rent arrears and you thought your partner was paying the rent, the council may consider your partner to be intentionally homeless, but not you.
One adult is not usually responsible for the behaviour of another adult. So, if something that your partner/spouse did led to the family being evicted, s/he may be intentionally homeless but you can make a fresh homelessness application
If you got into rent arrears or mortgage arrears because of genuine financial difficulties that were beyond your control, the council should not consider you to be intentionally homeless