The two cases are very different.
The first involves a debt collector entering onto property in connection with an allegedly overdue utility bill, which is something a debt collector ordinarily would not be permitted to do without a money judgment following a court proceeding and further court orders authorizing collection of the debt from tangible personal property on the premises.
This is pretty much completely without justification and realistically is a criminal offense as well as a basis for a civil lawsuit, although the modest money damages involved may have made such a lawsuit ill advised for the resident impacted by the unlawful entry.
Notably, in this case Scottish Power, "admitted the error, apologised and offered compensation." I doubt that an American utility company would have had the good sense and grace to act the same way. The story doesn't make entirely clear if these were Scottish Power employees or debt collection contractors hired by Scottish Power. The question implies that abusive utility company collection agents are a systemic problem in Scotland, although the article itself does not.
The second involves a utility company, Scottish and Southern Energy (SSE), drilling a lock to enter onto property in order to check a utility meter, in a building where some other tenant at a different address was not paying an electric bill on a different meter, which presents a very different issue. The customer at the address drilled had reasonably documented the utility company's mistake, but the company, for some reason, didn't believe the customer and didn't make arrangements to visit consensually when the customer was home. Instead, while the customer was work on Wednesday two male SSE workers drilled through the lock to gain entry into the flat, and when they got in and looked at the meter, they realized that they were mistaken.
The fact that the story describes the two men as a "warrant team" leaves open the possibility that a warrant for entry was received from a court based upon bad information from the utility company when it should have known better, although that issue isn't clarified in the story.
The customer “lodged a formal complaint against SSE for unlawful entry and reported the incident to the police.” And an ombudsman elevated the issue.
According to the utility company, it "offered to replace all the locks in her property and offered her a goodwill gesture payment of £500. Both were rejected by Ms Harvey who wanted compensation for further rental, hotel and new property costs which we were unable to agree to."
Utility companies will generally have an easement or some similar legal right to enter onto a customer's property to read a utility meter or the deal with something broken on the premises that affects the larger utility system such as a short circuit that is bringing down the power of everyone on the block, without notice in cases of emergencies.
So, in this case, the issue is not the absence of a right to enter somewhere, but the fact that the utility company went to the wrong place (where it may very well have had no right to enter because there may have been no utility meter to check at that location), which in and of itself, would be mere negligence if it hadn't received such clear communication from the customer and ignored it, and secondly, whether the method it used to gain access to the property in the good faith belief that it had a legal right to enter to gain access to the property was reasonable.
Charitably, it could be that the utility company had a key allowing it to enter and read the meter at the proper address, but that key didn't work because they were at the wrong address and the utility official may have mistakenly believes that the lock was broken rather than that the address was wrong. In that case, the question would be whether it was reasonable to force entry in a non-emergency case like a meter readings, rather than trying to contact the owner to resolve the question, which it probably was not.
It isn't quite as obvious that this would be a criminal trespass, because ordinarily entry onto property under a claim of right, even if mistaken in good faith, does not constitute criminal conduct, although a claim of good faith in a context where the company as a whole knew better even if the right hand may not have known what the left hand was doing, probably doesn't hold up under agency law that imputes the knowledge of any agent of the company to the company as a whole. But, while the company may have committed a crime, the two workmen detailed to do the work may have been acting in good faith personally, and may have even had a warrant.
Certainly, the utility company should have liability to repair any damage that was done to the premises in order to gain entry that arose from its negligence in going to the wrong address and its unreasonable failure to confer with the customer about the problem in a non-emergency. SSE would probably be well advised to admit with good grace that it was in the wrong and to pay the still very modest amount that the customer claimed for an alternate rental, rather than fight this issue where its fumbling became not just rude but abusive.