The law is:- 1.The grooves of the tread pattern must have a depth of a least 1 mm throughout a continuous band measuring at least three-quarters of the breadth of the tread and round the entire outer circumference of the tyre, OR 2.if the grooves of the original tread pattern of the tyre do not extend beyond three-quarters of the breadth of the tread (i.e. common with motorcycle tyres) any groove of the original pattern must have a minimum depth of at least 1 mm I tend to change about 1.5 mm - 2mm
Jamie's answer is by the book. Simpler answer is keep an eye on the tread wear indicators, and look for uneven wear.
I tend to work on the safe side. This country is temperamental with rain. Tyres are cheaper than skin! And you don't half feel a twat when you fall off. Mike.
I change, when it feels like a 2 stage drop when I tip in and the tyre has a profile of a 50p piece, tread depth really does not factor at that point.
As previously mentioned, there are indicators on most tyres now but i too go with the feel and shape ! If the back starts flatten noticeably it'll feel more sluggish as you lean it in and also drift a bit more when you give it some, and when the front starts to do that 50p shape thing then it'll step out on the front under pressure and thats never nice ! I still get a good few thousand miles out of my sportsmarts but I've learnt to go with shape over legal tread depts !