I'm amazed at the fabulous 'rights' people have! I worked in noise pollution for eight years, and I've never hard of any of these laws or rights! We had no end of trouble with wooden floors in upper flats, but we couldn't force people to put carpets down.
If noise is generated as a result of normal household activity (I.e. Walking around and living a normal life) rather than sheer inconsideration, malice, or any other 'reason'. People do have a right to live their lives too.
Often we had cases of basically, intolerance, people moving above a takeaway and not expecting to smell food till 11pm, or complete silence from the pub next door. Flats complaining about each other was par for the course. We would have families complaining about the 'smell' from the family next door, who culturally ate a lot of curries, or, when Ramadan was in the summer months and even the children had to rise before dawn, for food and prayers.
Its impossible to set standards as they are so variable, depending on the entire picture. The measure we used was that of a 'reasonable person' and within Environmental Health we were judged to be 'reasonable'.
In this case I would say (based entirely on the OPs info) that installing properly insulated carpets was a more than reasonable step to help her new neighbour. However, its unlikely to solve the problem entirely and mediation might be a more suitable intervention in this case.