I think you need to be a bit more understanding of their pleight and yes I know it's a busines not social work. What you need to do is help the tenant to get an increased housing rent allowance and you may have to threaten her with eviction if she is already at the ceiling. The councils have a system for increasing the 'official' ceilings where a family is going to be evicted, you need to explain this to your tenant and help her to get the paper work in order.
I don't know anything about timelines of notice.
And no I don't agree that tenants would have seen this coming a lot of social welfare tenants are living week to week. Sounds like a good tenant despite the arrears as they are making an effort, have been with you a while, they have redeocrated so really think long and hard before you think about really evicting.