You can update the settings for your iPhone and new SIM by connecting the phone to iTunes, this will update the carrier (or SIM) settings for you.
You can also change them manually by going to Settings > General > Network > Cellular Data Network > APN. For a Pay As You Go SIM this should be pp.vodafone.co.uk and the username and password should be WAP and WAP.
Once you've done that you'll also need to change the APN settings on MMS (just below) again to pp.vodafone.co.uk so that you can still send and receive MMS on your phone.
If you get stuck just give me a shout