Cat and emissions

[Prudie]

My car has failed its MOT on emissions (very high reading). The garage didn't have time to diagnose or fix so I paid for the full MOT and don't know what to do next. General opinion is it could be the catalytic converter and/or lambda sensor but should I get those replaced with no guarantee they're faulty or splash out for a diagnostics test first? It's all very expensive and very depressing. There's no engine warning light on (in case someone asks me). Can anyone advise?

[AlBags]

Well .. Good news TBH .. It could have been a lot more trouble than that.
There is going to be a coolant temperature sensor in the manifold or cyl head somewhere. Those usually tell the ECU the temp and the ECU decides what to do. Clever ECU's keep the mixture a little lean for the first minute or so to heat up the CAT quicker .. then adjust mixture towards a Lambda of 1 to get the emissions straight down.
Loads of extra fuel can kill a CAT long term.
A check of the MAF would not go amiss .. especially if it starts idling roughly or cutting out at junctions.

[Prudie]

Thanks, I will mention that to someone who might understand. It's been to 2 garages and I work with 400 mechanics (admittedly on tanks) and the 6 or so I spoke to all had a different opinion.
My conclusion is emissions are not well understood by the majority (and wondering if my MoT is a tad dodgy).