The kennelling set up you describe, in particular the location away from the house and the seeming lack of interaction with the puppies, makes me question if these are pets or the owner is breeding as you suggest. If they are breeding, there is potentially another avenue to investigate because breeders must be licensed by their local authority.
To be classed as a breeder though, the individual would need to be breeding three or more litters, and selling at least one puppy, in a 12-month period. If they are breeding only once or twice in a 12 month period a licence COULD still be required if the LA believes it is a business (fundamentally the LA would need to decide if the individual is “breeding dogs and advertising a business of selling dogs”).
If an individual is breeding less than three litters and selling without making a profit, a licence is not required.
Of course, they may be a licensed breeder, and the above is all immaterial, although if this is the case I’d suggest the dogs’ welfare might be paramount as other posters have suggested.
Also worth mentioning that LAs often allow people who are found to be breeding without a licence, to then become licensed breeders, so if they are unlicensed it may not resolve this issue. However, that would make the process significantly more admin heavy for your parents’ neighbours, mean that income isn’t invisible to HMRC, and might just be enough for them to decide it isn’t worth the hassle.
Either way, it’s not a nice situation so I feel sorry for your parents. Best of luck.
(Caveat: NAL, 15 years with a dog welfare charity)
(Edited because I had missed you have already tried talking to them, and tried raising a noise complaint with the council)
11th February 2022