UK Property Law
Get UK Property Law Questions Answered by Experts
Has she actually left your property?
If she is genuinely a lodger then you do have to give her notice as you have done and you do have to let it expire.
However, it is very easy to evict a lodger. You can literally just wait until she leaves and then change the locks afterwards.
In legal theory you could use force to remove her but I wouldn't recommend it. She will only start making allegations of disproportionate force.
Can I clarify anything for you?
Yes, you do.
The fact that she is a bad lodger doesn't mean she isn't a lodger.
You could sue her afterwards or deduct from her deposit.
Well, as I said really.
Give her the notice period and then change the locks.
Then sue or deduct from the deposit if there are arrears.