As you have discovered, your old new home has not been built to the standards required.
Firstly, there are no requirements for sound insulation between rooms in the same dwelling, other than to a bathroom or cloakroom.
Regarding the cold room, this should have been picked up by the original buyer and reported to the housebuilder and/or warranty provider.
After ten years, particularly as a second buyer, you have no recourse to either the original housebuilder or the warranty provider. You could try writing to them but I doubt very much you would be successful.
Buying second-hand homes, buyers should have a full structural survey.
Then if the surveyor misses anything you can then sue him for negligence.
Any surveyor worth his salt would carry out a thermnal imaging survey on any home built in the last 15 years, as time after time housebuilders have been caught out, having not installed insulation at all or it is only partly installed.