What an awful position to be in. I presume you've talked to the about the noise, distress and un-neighbourly situation.
OK, I shall be vindictive!
Does the local council know that the 'less nice' person is operating a business from home? It could affect his Community Charge.
Do the Benefits office have records on these people? Are they receiving any benefits that would probably be withheld if the truth came out?
Does HMRC know that (probably) there is earning going on without being declared?
Are they causing a health and safety or fire hazard.
And all backed up with photographs or videos?
Yup, I know it's vindictive, nasty and everything else under the sun; but it is not really the sort of thing that should be carried out in a housing are. Just accumulate the evidence in a secret, anonymous and underhand manner and report the matter.