Using the Internet on Iphone PAYG Vodafone?

I'm on PAYG vodafone and wondered if use the internet on it in my own home(I have BT Broadband) it will not affect the credit as I'm already paying for the broadband,
I have an ipod and when I use internet on that it doesn't cst me anything as obviously it doesn't have a sim in it.

Added (1). I hve my Wi-Fi turned on in my phone but I can't see a symbol ontop of the display

If the Wi-Fi is turned on your phone and you have the Wi-Fi symbol on the top of your display it means that you are connected to your home network and i won't take any of your credit.

If you are connected to your Wi-Fi at home your phone will always use the Wi-Fi network over the network data so you won't be charged for using your home Wi-Fi.