Paulscho,
To fly in the States you need to get a restricted FAA certificate on the basis of your JAR/UK PPL. Before that used to involve turning up at a Flight Standards District Office(FSDO) when you arrived in the US and getting your certificate.
However, security has been increased and the FAA now do background checks on all those wishing to fly in the US.
Here's what you have to do. At least 60 days before you plan to go you must fill in and send to the FAA
this form. In addition to this, because of UK data protection laws, you must also complete
this form and send to the CAA. If you don't your application will be delayed.
The FAA, on receiving your form and copy of licences and medical etc, will contact the CAA and verify the authenticity of your licence. They will then send a verification letter to the FSDO that you nominated on the form. They also send a copy to you.
When you arrive in the States to get your FAA certificate, the FSDO will first check that they've received the letter. If not you can't have the licence. It may be worth contacting the FSDO before you set off to check that they have in fact received the letter from the FAA.