The price shouldn't change in the second month.
I am assuming the order has gone through and already started with regards to the change of address and Broadband upgrade ?
if so when you go to your online NOW account under My Account > My Bills & Payments what price does it show for any up & coming payments ?
To be honest your best bet is to get back on the phone to the NOW Broadband Team where it sounds to me they have incorrectly charged you for the upgrade price promised.
When you phone them back and if you don't need the Anytime calls package you can ask for it to be removed together with the price relating to Anytime Calls if this is a feature you do not require.