Excluded occupier notice

[tissuesosoft]

Hi all
This is my first post here so will try not to drip feed etc.
I have the sole tenant. With written permission of my landlady I took in someone to rent the spare bedroom (I knew the flatmate beforehand). There was no written agreement or deposit (big mistake I know) and they are not named on the Main Tenancy Agreement or the protected deposit. The flatmate agreed to pay a certain amount but promised when the new bills came through she would contribute more. The new bills came in and she refused to contribute. I have been lumbered with all the bills and more than half the rent. She pays her rent to me and I pay the whole rent as one payment to my landlady.

My flatmate does not help clean (despite this being agreed to be split when she moved in) and I have become very stressed with the situation - I had to ask her to do basic things (such as washing up what she uses) etc, this is met with sarcastic response. This morning she left a blocked toilet for me to sort out...

She gave verbal notice mid July (after speaking to her again) that she will be moving out. Then via text to say she will be moving out mid August, followed by a letter. The rent is paid up to this period. However, after this morning's discovery I do not want to continue living in a place where she creates a terrible atmosphere.

I have spoken to CAB and Shelter. They have advised she is an excluded occupier (as she pays her rent to me I am her landlord) so there is no legal minimum notice I need to give back to her - it just has to be reasonable. Can I consider a week before the date she gave to be reasonable (and will give it in writing)? Which means 3 weeks since she gave verbal notice. I am willing to pro rata what rent she has paid to give back to her to cover that last week, but is that too much especially since she has not paid any bills?

She has no regard for my feelings or how she has treated me but I still want to make sure I do things right now. Thank you for your advice!

[tissuesosoft]

*I am the sole tenant. Sorry for that error!