If it was before 01/Aug/92, you need non-CAT test that looks for the CO/HC data only and not the lambda.
Your post suggested that the tester carried out the BET and not the non-CAT test so that's why I asked.
You may want pointing it out to the tester to check the spec of the engine based on the VIN.
Even if you failed the BET, that doesn't mean MOT failure.
They won't be able to find the exact match of your NSX for the combination of VIN and engine spec because it's 91 model registered in 93.
Even the VIN format for 92 model is different from yours.
Therefore, if followed the emission test screen, this should result in carrying out non-CAT test.
It's like having replacement engine from earlier model on the later spec chassis.
[Edit: Graham, if you send me an email at kaznsxcb-002'at'yahoo'dot''co''dot''jp' , I can send you a document showing the VIN and Eng no. combination for 91, 92, 93 models that may help in assisting your claim.]
If failing to convince the tester, then as others suggested, just keep the CAT really hot.
The emission test procedure is within the closed loop control region and because of the delay in the sensor as well as the in the feedback loop, several small factors will add up to hit the limit.
Old fuel doesn't help but again, keeping the CAT hot is the key.
You are allowed to drive the car even after the MOT expired as long as you can prove that you are on the way to take the MOT. You can book for MOT and ask the test station to send SMS/email/etc as the proof in case you were stopped or caught on road side camera for some reason.
Kaz