It would certainly do no harm in the event that she obtains possession again.
If the condition of the property has deteriorated owing to acts of waste by, or neglect or default of, the tenant then you can also serve a s8 ground 13 notice on her for which the notice period is only two weeks.
So if I serve a section 21 and section 8 notice, can i apply for a possession order after the expiry of the section 8 notice period or would I have to wait until the section 21 notice period expired?
You could apply for possession on the basis of the s8 notice once two week notice period has expired, provided you can prove the ground (ie deterioration as above).
The difficulty is that if a hearing is schedule and the tenant attends court then she will bring the issue of the illegal eviction to the Courts attention and they will be disinclined to make an order. You can serve the notice, but it may be prudent to wait and see what her next move is before applying for an order. Ideally she would drop the issue, find a new property and not sue you.
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