UK and EASA used to be one and the same. Now they're separate but essentially still the same. As an ICAO ATPL holder you can self-certify for the exams so you don't need to do a formal course at an ATO.
1) Get a pair of class one initial medicals to determine your state of licence issue. This can be a show stopper.
2) Do one set of study and take each exam twice. There are plenty of online question banks and study guides.
3) Your license skill test can be your next LPC if the examiner is qualified and you have 500 hours on type.