thanks for all the help!

Hi, I apologise in advance as i'm sure this question has been asked before, I really need to make sure my thinking is correct before challenging my landlady (again). I've been in my flat for around 22 months now and began with a fixed term AST for 1 year with monthly payments. The only Termination time was at the 6 months "Break point" and included a 2 month notice period. At the end of the year the landlady and i agreed to allow the contract to roll on a monthly basis (for the past 10 months). On the 12th June I gave written notice saying I'll be out of the flat within one month (also aligned to the date of rental payment). She replied saying that i had to serve two months notice as in line with the original AST. I checked the contract and according to that it states: "16.2 If the Tenant stays in the property after the Tenancy has expired then a statutory periodic tenancy will arise on a monthly basis". Having done some reading around my understanding is that the tenant only has to provide one months notice whilst the landlady is required to provide two months notice in the case of defaulting to a a statutory periodic tenancy. Is this right? I'm hoping to go back to the landlady and say. Here's my contract saying i am on a statutory periodic tenancy, i have no obligation then to serve more than one month of notice following my last rental payment. I have quite a big rental deposit that i could do with so don't want to become embroiled in a war over it! Many thanks in advance.