I did a lot of searching for something equivalent to the options Americans had just buying Vanguard. Somehow I stumbled on the term non-resident alien (NRA), which is anyone living outside of the US who isn't a US citizen. That lead to a lot of really well written wiki's and forum posts on the bogleheads forums. There are a few options for NRAs, but the one most recommended by the bogleheads, and on a number of other sites was interactive brokers. I also liked that their monthly fee is waived if you have $100 000 invested with them.
At the moment I just have new money in their account, so it's not my R1m by quite some distance, but the account is ready and waiting, and should I need to move the funds I'll be able to. I'm also fortunate to have a US bank account, but they take transfers in all major currencies, so an EU, UK or even local bank offshore account would be perfect.
I was close to moving all my cash in December after it looked like we were heading downhill fast, but I couldn't bring myself to pull the trigger. All the reading material says the dollar is overvalued, and the rand is undervalued, and I just couldn't swallow a hit that big. I even went as far as getting my tax clearance, almost. It turns out you can't get tax clearance for investment without going through a bank/broker, but the lady at SARS did confirm they would give it to me with the documents I had on hand. We'll have to wait and see which way we head.
Eventually all my investments will sit in interactive. If I decide I want to hold South African shares, I'll just buy the iShares MSCI South Africa Index Fund, or buy dual listed shares, but I think once I'm out I'll be staying out.