Notice period 2 months?

Hi, I was wondering if anyone could help, we have to give 2 months notice on our rented property which just isn’t suitable for us. I am getting conflicting information online about whether we have to give the 2 months notice or not or whether we can get away with 1

Our lease ran from 30th jan 2016 - 30th jan 2017. It was never renewed. Here is a small extract of the lease in regards to notice

The period of let is from the date of entry to the date of termination, after which it will continue month to month subject to either party not giving less than 2 months prior written notice at date of termination or on the 30th day of the month thereafter.

I think we are on a short assured tenancy as we were given the correct form for that. Do we have to give the 2 months notice?