RetireJapan

Just wanted to add my experience. About 6 months ago I successfully applied to pay Class 2 voluntary contributions. Many thanks to all the advice and info here. I also applied to back pay the last 16 years of contributions but was waiting for the yen to improve before I transferred from Japan (Yeah that went well...)
As I am back in the UK at the moment I decided just to transfer it from my UK bank noting the slightly different bank codes for paying in from UK vs Overseas. Having done that I wanted to call and speak to a human to confirm the payment had arrived and for which years. I tried the 161 931 9070 number first, on hold 20 minutes, but they said they weren't able to check my records on their system and to call the 0300 number or the 191 203 7010. I tried the 191 203 7010 first (on hold 45 minutes) and the payment hadn't showed up yet was told it would take a while longer as all payments go into a holding account before being directed/credited to the individual records. Up to 8 weeks before it would show up online. I did manage to have a note attched to my file that the incoming payment was for the last 16 years so that was something I guess!

Maybe this has already been mentioned, but you can now register for voluntary national insurance contributions online.

I just did it and it's very easy.

FWIW I have been paying voluntary class 2 NICs for almost twenty years, but about three years ago they stopped taking the Direct Debt and I have just gotten around to trying to sort it out. I was expecting to have to call and hold or write letters and wait months but it is great that it can all be done online, and you get a reference number and confirmation number that they have the application.