Without being in the car it is hard to diagnose the noise.
I would like to think an efficient Mot tester would have located the noise in the test.
However, a light annoying rattle from the front end can be an anti roll bar link, this is a short rod about 8 inches long usually vertical from the thick antiroll bar down to the bottom suspension arm/wishbone, with the car sat in a flat road sometimes you can grip it and rattle the joints to feel excessive movement.
The antiroll bar itself can give a softer deeper knock from it's mounting bushes on the chassis, it goes across to both sides of the car and transmits loads from one side to the other.
A sharper knock can be the lower wishbone inner mounting insecure in the subframe.
The lower wishbone outer ball joint can give a knock at low speed on full lock.
A broken spring coil would give a ringing rattle but the Mot tester who misses that would want their "arse" kicking"
Top suspension mounts usually make a noise noticeable on low speed turning plus you may feel it through the steering wheel.
Re dampers/shock absorbers, if just weak then not usually noisy but if the rod is worn in the bush/seal support area it could rattle but not common.
Track rod ends and inner track rod arm joints can rattle, but again a Mot test should show that.
Can you hear the noise from one side only? I have even driven on a quiet road mounting the pavements at low speeds and dropping off to pinpoint one side or the other sometimes.
Another point unless car is jacked up in the position to show that particular fault suspension tension can hide it, so not necessarily makers "jacking" points.
Many years ago as a foreman of a dealership I had an Mot tester with years of working in the trade miss a badly worn joint, that I picked up when checking a brake fault, simply because of not understanding the suspension operation on that make of car and yet that was a common fault on that make that often resulted in the suspension collapsing leaving the car in the middle of the road!!!
Over 50 years in the motor trade I have come across 100s of noises, from loose wheel nuts/bolts down to a metal choke cable rattle due to a missing grommet in the bulkhead.
If you are a reasonable DIY mechanic then I suggest you look for some of these faults in descending order.
Failing that, note exactly when it makes the noise and what side if possible and go to your trusted garage, speak to the mechanic doing the job and give him the full information to help diagnose the fault. If a different garage to the Mot Station you could tell him the noise has been happening for a while but nothing showed up on recent Mot inspection, to give him a challenge to prove he is better than the tester.
