Here's a quick report on what I actually did, in case anyone finds it helpful in the future.
1. I decided not to open an account with Prestia. The main reason was that the average monthly balance had to be over 50 man (500k) yen, otherwise they charged a maintenance fee of 2200 yen per month. I object to the principle of this so didn't bother.
2. Instead I got a "Certification of the Balance of Deposit" in English for my Post Bank account from the local post office. I was a bit worried that the address didn't include my postcode (field on the computer system not big enough, they said), but this wasn't a problem in the end. It took about an hour and cost 1100 yen.
3. I checked with the overseas bank (based in the Isle of Man) if it was OK for the UK post office to certify the copies of my documents rather than the strict list of professionals they gave. They said sorry but NO! The Isle of Man law didn't allow this. Blimey, good job I checked.
4. They then dropped the bombshell that I could certify the documents myself by email using e-KYC. WTF!? Why didn't they mention that on the wesbite or form? All I had to do was scan the two documents (passport and bank statement), and provide two selfies of me holding each one, such that both my face and the writing on the documents was clear.
5. So I did all that, and sent the application form by email that I had downloaded, completed and scanned (they require a "wet signature" so I had to print it, write it in ink, then scan it).
6. About a week later they said that my application was successful and I could fund my account.
So that was it. Relatively cheap and painless in the end thanks to e-KYC I hope it goes as smoothly for you too.