Advice regarding tenant who has complained to enviroment health

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My current tenant is on a periodic tenancy as the ast fixed term has expired last year. For the last few month she has delayed rent regulary by upto 2weeks but paid. She pays monthly and i had given the property to her under market value as condition is not great, but decent, ie brand new bathroom n wc, but dated rooms and decor.

Anyway she has mentioned to me few months ago there is seems to be damp issue but she wasnt concerned.

Today ive found out she has complained to the council enviromental health and they will come to inspect property next week.

Rent payment for this month was due on 19th but has not paid and said she will on the 31st as shes findind it difficult.

Shes text me today to tell me her health is affected due to the damp.

Please advise what i should due, ive been doing her a favour letting her rent at very low rent.

Either way ill have to fix the damp issue, however i dont want her in my property anymore.

Should i evict her under notice to quit or under section 21 requiring possession, or is she not breaking our periodic agreement as she has not paid rent thus can i evict her.

Under 21 i have to give 2 months notice but i think she wont pay.

Whats the quickest way of getting her out, also bearing in mind i dont want her to take me to court in regards to her health, in think shes trying to pull a fast one.

Please help