Agree, this does sound like a labral injury. If you are seeing a physio there are a couple of test which they should be able to do to check this (p.621 Orthopedic Physical Assessment, Magee).

The only other thing that springs to mind is psoas weakness (muscle controlling hip movt) from a possible overstretching injury during a kick. This causes a similar clicking, would notice if laying on back and lifting leg up then lowering back down (with leg straight)(click tends to occur on lowering) (obviously not definitive test). Does tend to be more noticable with slow control movement. Again physio should be able to check this for you (can correct momentarily with maximal hip suck type exercise, which can confirm whether this is a problem) if it is then needs retraining.

Best bet is to see a good sports physio and get a more definitive diagnosis / steer as to what needs to be done / how you can improve things.

Having done some kickboxing and karate myself don't be tempted just to ingnore the problem and just do quick kicks (because they are not so problematic), if you can't preform slow controlled kicks then chances are you are aggrevating the problem further with quicker kicks (as they are generally less controlled and snapped in and out). I carried on training with a hip problem for a couple of months (despite being a physio...i buried my head in the sand and ingnored it), then needed to take out more time than I should have to sort my resulting back problem out!

Good luck