This is one of those ambiguous, yeah-but-no-but areas where there is no single rule, but a lot of laws which overlap and essentially ban the modification of an exhaust to be noisier than standard.
For example
The Motorcycle Noise Act 1987 forbids the sale or supply of aftermarket exhausts that are non-compliant with requirements on design, noise, labelling etc. No specific noise level is prescribed though.
Section 54 of the Road Vehicles (Construction and Use) Regulations 1986 tells us that an exhaust is required to be fitted and it must not be modified to increase noise. Again, no limits but note the reference to EU directives.
In
section 2.1.1 of COUNCIL DIRECTIVE of 23 November 1978 on the approximation of the laws of the Member States on the permissible sound level and exhaust system of motorcycles we finally come up with some limits:
So, in summary, the type approval requirements have limits and other laws prevent you from selling noisy exhausts or from modifying your exhaust to be noisier than when approved. Finally, the
MOT takes a typically vague and subjective approach which requires the tester to make a judgement as to the level of noise compared to "
... a similar motorcycle with a standard silencer in average condition."
But as we know, all of these laws and regulations are broken - you
can buy a noisy exhaust and whilst it may be marked "not for use on the road" or simply devoid of the required regulatory markings, people do use them on the road and the chances of being caught and dealt with are clearly low enough that it is done regularly and with little thought to consequences. Bike-friendly MOT stations will let them through on a nod and a wink.
I did once replace my exhaust silencer for a sportier-sounding one but made sure it was BS-marked and nominally road-legal - it retained the silencing baffle and whilst sounding a bit fruitier than the standard one, was not at all obnoxious - I was as much interested in the smaller size and reduced weight as the increased noise.
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