The legal minimum tread depth for cars is 1.6mm in a continuous band around the centre three quarters of the tyre.
Should you be found with tyres below the absolute minimum, then you receive a maximum of 3 points on your license and up to a £2,500 fine (£5,000 in the case of a goods vehicle).
The easiest way to check your tyre is with the 20p test
Take a 20 pence coin and place it in the tread of the tyre. If you are unable to see the outer rim around the edge of the the coin, then chances are it is above 3mm. If you are able to see the rim, it is likely to be below 3mm and needs to be checked by a professional.