Can a Mobile Phone branded 'Vodafone' be used on another network?

[Nick]

I believe it is the phones internal serial number (IEMI) which is hard coded into the hardware that is sometimes locked to a network.
If the phone is reported as stolen to the current airtime provider, then they can mark the IEMI on a central database preventing it from ever being used on any network again.

It's actually called an IMEI (International Mobile Equipment Identity) - a 15 (or 16) digit GUID (Globally Unique IDentifier).

Typically, on the phone keypad, type '*#06#' - you should then be presented with your phone's unique identifier.

You can then type this number into a checking website, like http://www.imei.info/ and http://www.imeipro.info/

Note that there is no obligation for a supplier to mark a phone as blacklisted when it's reported stolen, so these checks aren't 100%