Hi @OneTwoStep sorry to hear you're having a hard time. I'm very lucky that I have private cover through DH's work so I only had to pay the excess as the GP was happy to refer me.
I think an initial consultation is usually somewhere between £180-£250 plus the cost of tests. The tests are where it can get really expensive.
If you can afford it, and already have some test results you can share with a cardiologist, it might be worth an initial appointment just to get the quick view on whether any significant concerns - and if he/she suggests extra tests that may become expensive you have something to go back to the GP with to ask for a more urgent NHS follow up.
Perhaps as a first step (as usually you will need the GP referral to get a private appointment, although recently I have had appointments before my referral letter has arrived and no one was bothered, it may be more for insurance purposes) ask your GP surgery for a copy of your NHS referral letter from GP, your blood tests (even if normal) and the ECG if you can get it. Ask the surgery if they can recommend someone good locally (mine almost always can) and then call the consultant's secretary to ask about appointments and costs.
I am still not totally convinced my heart is completely ok given some of the symptoms I have had, so I understand how you might be feeling with what your ECG showed. I would hope that the nurse who looked at your egc would have said if she felt it needed very urgent review by a cardiologist, but if you can speed things up then definitely worth a try if it won't bankrupt you.
I had a very odd reading on the Kardia monitor when I was having what felt like severe palpitations and the monitor flagged it was abnormal. When the GP looked at the reading he said it was normal... Fingers crossed everything is ok - good luck getting to see a cardio. Take care x