You can do it on the NHS, but will take long time.
Private for the test to be done will cost more then £300 with aviation cardiologist. I do not recall all the details, I belive just the letter (report from the doctor cost £220 - the consulation)
Then you pay for each of the tests you need to do, Echocardiogram was £375, exercise Electrocardiography was £280, + the 24 hour Holte test, do not have the cost of that, but would probably be another £200 - £300.
This was by an aviation cardiologist - no way will you get away with all those tests private for much less. I could have got all trough NHS, but GP had to refer you, and by that time and you get appointment, it can already have passed 3 - 4 months.
I bit the bullet, and then I am told I did not need to be investigated. Anyway best of luck, but at least budget with around £1000, I phoned several of CAA's doctors, and it was all more or less the same price.