Client for 6 years and we stick to the script

I have been a customer for 6 years. I am moving, so I decided to shop around due to several recent rate increases. I called to cancel on 2 May to give my calendar month as 1 May was a public holiday. The call centre agent said this would not be an issue due to the holiday. They now insist on invoicing me for 2 months, as I did not cancel on a holiday! The agent helping me has been no help, only sending me generic answers and templated responses with no actual help. Disappointing guys