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No. MOT test fees are VAT-exempt; therefore, no VAT is added to the cost.
The Driver and Vehicle Standards Agency (DVSA) sets the maximum fee garages can charge, and for a car this is currently £54.85. For a standard motorcycle the maximum is £29.65.
Garages can charge less than the DVSA maximum to stay competitive, but they cannot charge more.
As the test fee is VAT-exempt, what you see listed is the full amount you’ll pay. There is no extra VAT on top.