Thanks for your question.
I can confirm that because you live in the same property as your landlady you do not have the same rights as a tenant under an assured shorthold tenancy, unfortunately. Your landlady is correct. You can be asked to leave on reasonable notice.
Do you have any questions or queries in relation to my reply? I am happy to assist further.
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You share facilities and the landlady lives in the premises. You would be regarded as a lodger, not a tenant.