Hi Simon, ah! The great topic of muting.
OK, I'll jump in and probably confuse you no end, but I offer such value for money!
Right. Let's take a chord with which you are familiar, The A Chord.
Here's how I mute it "most" of the time. I use my Left hand thumb to rest on the Bottom E (Thickest String) so that it deadens the string and just produces a Thunk when hit.
Now, if you want to try another way, try this little exercise. Hold you A Chord. Mute the Bottom E as described, and do a Downstroke with the Pick, then, do an Upstroke, but now relax your grip on the Chord so that you just get a Thunk, then Downstroke again but gripping the Chord again.
All takes practice but works a treat.
Now, to continue. Something that many of us do, where is your right hand when playing a Chord? Try resting the heel of your hand on the upper edge of the Bridge, just rest, don't force your hand down. Now once that feels familiar, make a fractional movement of your hand and you'll find you can mute strings there too. This is a popular trick with The Metal Boys and that's what produces that Thick, Percussive sound. Try holding an E Chord and muting the Bass E and A Strings whilst you play that chord. This works best with Gain on the amp for instant gratification, but works equally well when played clean as this allows you to hear what's happening better until you feel you have it mastered.
Give it a try.