In answer to my own question, yes you can wash your mats in the washing machine. I did mine today and they came up like new. Or should I say were like new until I tumble dried them for too long, or on too high a heat. The glue that holds the edging on melted, resulting in some on it that's peeled away or got rubbed off.
Next time, I'll wash them just as before, but let them dry in the airing cupboard.