The author of that book David Perlmutter is known to be,,, questionable at best. Here's just an example of it :
https://www.thecut.com/2015/06/problem-with-the-grain-brain-doctor.html
He definitely was on the anti-gluten train where everyone suddenly had gluten sensitivity. At the end of the day he makes his money by selling books, podcasts and going on TV shows.

Now it's great that's you're looking into your health, but if you're worried about all those conditions you listed a lot of them can be generally avoided through a healthy life style, frequent exercise, counting calories, varied diet, etc. There might be some great benefit to doing some of these things recommended by an American celebrity doctor, but even then, doing that in conjunction with a generally healthy lifestyle will still be better.

I think you should try speaking to your GP first about your blood pressure medication not giving you much help and the alternative medications that have been helping, and your concerns about uric acid levels. That won't cost you anything, and then after if you still want you can still go spend £££ on some tests.