I need to phrase this carefully, but it's not entirely unknown for a testing centre to 'cheat' to give them a reason to sell you a repair. This actually happened to a friend of mine; they failed a car on emissions and charged an extra £180
to replace a lambda sensor. As far as I could tell, the results were no different after they'd fitted the new one and it was out of limits when retested, but they reran the test and pronounced it within limits. I've heard it said that not fully inserting the testing probe can produce a similar result, as can allowing the car to cool down before testing.
If you google "MOT emissions lambda scam", the results make interesting reading.
I'm not saying that's the case here; many cars are legitimately failed on emissions; exhausts can leak, and lambda sensors can go out of tolerance.