Cancelling ESAT dial-up a/c

Looking at some threads on AAM, it seems esat/BT can be problematic to deal with.
Thinking of cancelling longstanding dial-up Net service with esat and going with the Eircom landline/broadband "bundle".
Should problems be anticipated in cancelling with esat and connecting to eircom? Is there likely to be either a gap or overlap in service?
What should we be prepared for? How best to keep disruption to a minimum?

Was this a flat rate or low call cost dial-up package or something? If not then it seems surprising that you were paying a subscription for a dial-up package this day and age. If you cancel maybe you could use one of the [broken link removed] if you are stuck?