Did you buy the gun first hand or second hand? If first hand (I'll be assuming it's still in warranty based on the fact you've only just complained) I'd get in contact with them and explain the issue.
If second hand, I'd text/email the person you bought it off and ask if they had any issues with this. They might lie and say no even if they did, but worth an ask as they may know about a little kink in the gun that can help.
Now: as an L85 owner myself (granted not an ICS, but the rough knowledge should pass-over) I know that the mag well can be a bastard on SA80s.
Clear out the mag-well, get a bright torch and look into it. You should be able to see the mag-release catch (if you can't, keep pressing and releasing on the mag-release button and you should see something moving.). Try and follow the mag in and see if it clears pass the catch. You should also hear a click. If it doesn't, the problem is with a) the Mags (unlikely seeing as the mags that it came with should work) or b] the mag catch.
I'll go with the most likely issue first: the mag catch. It MAY require it to be filed down (this was initially suggest to me however I decided against it.) Should be a relatively easy fix.
If it's the mags themselves. Which it shouldn't be, but if it is, follow it in and see if it's catching on the mag-well itself. You may need to use pliers on the rear of the mag to get them to fit. This is what I had to do.
TL;DR
- Figure out what issue is. If mags - they may need resizing. Use pliers on the appropriate area. If mag-catch - may need filing down.
All that said - if you hear a distinct click when you put a mag in and it still doesn't fire, that indicates it's probably a hop-up issue or something internal. Of which I'm learning, but useless at non the less. If you're not hearing a click, my issues are possibilities.