The regulations are written in a style intended for manufacturers and retailers rather than the end user. If a silencer meets the required level of noise reduction then it is stamped BS AU 193, otherwise it gets "not for road use" or "pre 1885 M/Cs only" according to the level and intended market. However, the stamp applies to the unit as sold… if it has removable baffles and the end user takes those out, the silencer may (i.e will almost certainly) be too loud to pass the relevant noise limit.
Since it looks like you could drop a ping-pong ball through that Carbon Can Company silencer it'd be very surprising if it's within the limit. The fact that police don't carry dB meters means you're unlikely to have a problem unless you make a nuisance of yourself, but you might need a lenient MOT tester.