These cheap code readers use the EOBD/OBD2 protocols for reading fault codes.
These protocols are required by law and are well documented, so usually they get the codes right.

Can you also read live data?
Then note all data that you get on idle, raised rpm (around 3000 rpm) and while driving around 50 mph.
Post the data here. Or get a gas analyzer test (like the one done with the MOT) and post all data here.

Have you checked for fuel leaks? Maybe the engine doesn't use all the fuel, but a part is spilled?