Does a Tenant Have to Give Notice Once Served a Section 21

I know a tenant at a property where the landlord has just served her a Section 21 (03.03.23) as she needs to sell up to pay off her interest-only mortgage.

Having been told by the landlord that it would be best if my mum found somewhere asap so they could crack on with viewings etc, I've managed to find her alternative rental accommodation from 31.03.23. Still, her landlord requests a month's notice from today, 06.03.23, until 05.04.23. Her current rent period runs 18th to the 17th of each month.

Am I correct in thinking that since the current landlord has asked them to vacate via Section 21, she should pay her rent as usual on 18th March and be refunded any rent paid from 31st March to 17th April? Or does a tenant still need to give one month's notice to end the tenancy despite being served a Section 21?

The month's notice her current landlord is requesting from today would surely be considered invalid as it is not as per the correct date as per the tenancy.

This is the email received from the landlord

"Thank you for your email.
Please supply, in writing (email), 1 months notice from , as from today 6th March 2023, to vacate 5th April, 2023.
Any rent due from rent day 18th of month, can be calculated on a daily basis should 's move be delayed.
Happy for her to be there until a buyer is found, if needed.
You and I will then need to meet there to do a check out & inventory, prior to deposit being made available."