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No, you can't take your car to just any garage. Only to certified MOT centres.
Remember the following:
If your car fails its MOT, you can get it retested for free at the original test centre - if you return it within the next working day.
You can only do this if your current MOT certificate is still valid. Or as long as the MOT test didn't report a dangerous defect.
If you have the repairs done at a different garage, you'll pay a partial fee for a retest at the original test location.