It is a legal requirement under UK law that the correct size and type of tyre is fitted to your car for the purpose it is being used for. This also includes you ensuring the correct tyre pressure is on them. so if you get stopped by the police for driving around with a flat tyre you now know why.
Now the exciting and most argued about part, yes the legal limit is 1.6mm of tyre tread. That is the minimum amount of tread your tyres should have, it needs to be 1.6mm across three quarters of your tyre so if half your tyre is below 1.6mm your tyre is illegal.
The penalty for having worn or illegal tyres on your car is 3 penalty points and a fine of up to £2500. That’s per tyre so you could potentially end up with 9 points or more depending on the circumstance you find yourself in.
After reading the above we would recommend you change your tyres at 3mm, all tyres come with tread indicators on them and it is something you must keep an eye out for not just because of the fines and points you can get but also the fact that tyres with a little tread means less grip which in turn means your car is less safe. Braking distances will be severely impacted with low tyre tread especially on wet roads.