I see your mechanic has polished the outside of the headlights to remove haze due to UV degradation of the plastic coating.
If misty inside, it is caused by condensed water vapor and means the seals are leaking. I've cleared some by removing the bulb and any rubber seals and allowing the light to sit overnight till the moisture clears. You can hurry the process by directing a hair dryer on low or no heat into the back opening where the bulb normally lives.
Afterwards, you can use a flowable clear silicone caulk to seal the seam between lens and reflector body. This usually cures the problem.
This may get you past the MOT/NCT, but it also means you will really need to replace the headlights if they don't remain clear after all these efforts...for safety because misty ones won't allow you to see very far.
All the best,
Dan.