You need to have your foreign licence verified by the FAA.
The below link has the instructions of what must be done. It also details additional information required for UK CAA issued licences.
Airmen Certification ? Verify the Authenticity of a Foreign License, Rating, or Medical Certification
UK CAA:- Complete the form allowing them to release your information to the FAA (SRG1160) and complete the payment form (SRG1187). Send this back to the CAA by post.
FAA:- Complete the Form "VERIFICATION OF AUTHENTICITY OF FOREIGN LICENSE, RATING AND MEDICAL CERTIFICATION". Sign and scan and email back to the FAA. The email address is in the link above.
FSDO:- Contact the FSDO once you get a reply from the FAA to say all is well and schedule the appointment. They should tell you the exact information they need, licence application, log book, medical etc.
FSDO:- Turn up at your allotted time and get your temporary airman's certificate. It is valid for 60 or 90days or something like that.
The plastic card will be posted to your home address.
Take your BFR.
Go flying....