CDs are not regionalized. So, your American CDs will play just fine in a UK player, and vice versa.
As far as phones go -- you're best bet is to buy a phone here. They are not expensive. Apparently there is a difference in rings and other things that will make a US phone not work quite right in the UK. Also, the plug-in to the phone jack is different in the UK. Mobile phones can be expensive, or not expensive. I bought a pay-as-you-go phone the first week we were here. I spent 99GBP on the phone (could have gotten an phone for 69GBP, but wanted a different phone) which had a pay as you go plan. Walk down any High Street and you'll find multiple mobile phone retailers. For me, pay as you go works best. I don't use it that much, simply have it on when I go out of the house during the day (in case school calls), or when I travel. I don't make that many calls. OK, the first month I made a ton of calls, but that was because that was our ONLY phone for the first month , so we used it for everything, including calling back to the States.
HTH,
Stephanie