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Yes, you are allowed to watch whilst your vehicle is put through the MOT test. However, you are not permitted to interrupt the tester during the MOT test.
Alternatively, most MOT centres have a waiting room where you can sit and wait.
If you can't wait around, you can arrange for someone else to take your vehicle to the test centre if they are insured to drive it.
Some MOT centres may also be able to collect and return your vehicle.
You can get an MOT up to one month before it expires and keep the same renewal date. You must renew your MOT before it expires.