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Most tyres have a built in wear indicator. It is a small raised "bead" in the tread groove which is 1.6mm high. The tyre is deemed beyond service when the adjacent tread is to this marker. It should be changed immediately at this point. A new tyre has approximately 8mm of tread on it.
The current legislation is that the grooves should be 1.6mm throughout a continuous band comprising the central three quarters of the breath of the tread & around the entire outer circumference of the tyre.
The tyre should not display any damage which is more than 25mm or 10% of the section width. No internal structures of the tyre should be visible. There should be no lumps or bumps however caused. Inflation pressure should be as per vehicle hand book.
Do note that fines (upto £2500), points & disqualification can be handed down by the courts. Each tyre will be deemed a separate offence.