Scrub the mussels in cold water. Scrape off any barnacles with a knife, then pull out and discard the fibrous beard visible between the hinge on any of the shells. Discard any mussels that are not tightly closed, or which fail to close when tapped sharply.
Heat a large wok or pan over high heat and then add the oil. Stir in the garlic, ginger, chillies, and spring onions and stir fry for 30 seconds.
Grate the rind of the limes into the ginger mixture, then squeeze both fruit and add the juice to the wok with the coconut milk, soy sauce, and sugar. Stir to mix.
Bring the mixture to a boil, then add the mussels. Return the pan to a boil, cover and cook briskly for 5-6 minutes, or until all the mussels have opened. Discard any unopened mussels.
Remove the wok from the heat and stir in the chopped cilantro. Season the mussels well with salt and pepper. Ladle into warmed bowls and serve immediately.