I followed @Anahata's advice and used some Ivory soap plus some luke warm water and a dish cloth. I needed to give it some proper elbow grease and not be afraid to give it a really hard scrub to get the film off. With enough water you'll create some of that white sudsy stuff, I then used the hard side of a washing up sponge to give it a further scrub before wiping off any remaining soap with clean water. I found after leaving to dry, my mat was a lot more grippy slippy, but my hands still slipped a little. So I also bought some rosin to use with it and combined with the scrub method - it's pretty good!
I think I'll give it a salt scrub too and am confident it'll be just fine after this. The improvement I've seen so far has been significant from the soap scrub but it does need a lot of effort to get this horrible film off. Pain in the bum but worth it as I find this mat (Prolite) super cushioned and lightweight for it's thickness! Thanks for the tip @Anahata