What is the cheapest way to send money from the UK to Mauritius?

The cheapest method would be a Bank Wire Transfer. Bank Wire Transfers are based on a fixed price, and is converted at the official rate in Mauritius. Western Union and others will have a very hefty charge, as well as conversion at a rate lower than the official amount. Hence, it would make perfect sense to use the legalized banking channel to send your money. Also, I think Western Union or Moneygram might have a limit as to the amount of money that can be transferred.