I am afraid you have to compy or recieve a summons for non comliance.
If the officer believes your car is not of legal standard, then they can give you a rectification order which is what you have. If they have test equipment, then they can test in the roadside and issue a fine there and then.
in your case, Legaly you must replace the back box and have an MOT station check it and stamp the form, you then send it to the address on the form.
Nothing else happens, you get no fine nor points.
However, if your exhaust isnt that loud, then have the MOT check it, (normally they will listen and if its not obtrusive you will be fine) and thats it.
If your exhaust is OBVIOUSLY way loud, then you might get stopped again.
After three times of being stoppped for this offence, you can be prosecuted and the car siezed and crushed.