Yeah, just ring Wannadoo and ask them for your MAC code. They might take a little while to get it to you.
Once you have it, ring up the other provider (or better imo, use their website) and sign up and MAKE SURE you give them the correct MAC code - mistakes here can screw things up a lot.
What you may want to do then is cancel your direct debit or whatever to Wannadoo - lots of ISPs 'forget' to stop charging you and it's a lot of hassle to get the money back.