My tenant gave me just 8 days notice – help please

I am a relatively new landlord and have a tenant who wants to leave : she emailed me on the 19th Feb and wants to leave by the end of the month, 28th Feb. 

The notice period is not explicit in the AST agreement but it does clearly state that the rent is payable monthly, 17th of each calendar month (which is the AST start date).

She paid cash for the first months rent but asked if she could pay weekly thereafter as that would suit her working position better than monthly payments. I agreed, though no changes to the AST were made. She has been in the property just on 9 months.

She has been told by a letting agency, presumably while looking for a bigger house, that she only needs to give one weeks notice as she pays weekly. I think she should give me one months notice as the original AST states monthly rent payable.

When her 6 month AST tenancy ended I have assumed that her contract is monthly and this is what the AST states, regardless of when she actually pays the rent.

The tenant and I have not discussed this at all.

Any help or advice would be greatly appreciated, as it is now she has effectively given me 8 days notice!

Many thanks

Denise Dee