Two issues:
1. There could be a Housing Benefit problem as she should have been declared as a non-dependent, which would probably (based on her income etc.) have resulted in your Housing Benefit being reduced - the assumption being that she would have been paying you something towars the accommodation. I doubt whether there is anything you can do about this - you either just hope the benefit people don't find out, or you tell them now (with details of her income), find out how much they want to reduce your benefit by & get her to pay you that amount.
2. Your concern about sub-letting. To me, it doesn't look as if anyone could reasonably accuse you of that - what you've done is to have someone staying with you for a temporary period rent free. If you are a private sector tenant the council will not be interested anyway. If you are a social housing tenant then - if it is raised - you need to explain the situation, which seems to me to be little different from someone who has a friend come to visit them for a period. If you wish (& you want this person to leave), you could write something on the lines of what she is asking together with an explanation that she stayed with you temporarily & you can no longer accept this. In effect, you are saying the same as saying she is being evicted without using that word - & there is no reason why you should not tell her she has to leave - you have no legal obligation to her other than to give her a very brief period (probably no more than a week or two) of notice to leave.