That is an important point. Unlike the Netherlands or some other countries, there is no official definition of "membership of the Royal House" in the UK. There is only a loose definition of the Royal Family, which seems to be based on proximity of blood to the Queen rather than whether a person is an HRH or not.
"Membership of the Royal House" is actually a tricky point as it doesn't follow a uniform rule on an international basis. For example, in Spain, there are HRHs like the Infantas Elena, Cristina, Pilar or Margarita who nonetheless are not (currently) members of the Royal House. Conversely, in the Netherlands, before Queen Beatrix's abdication, there were non-HRH like Prince Constantijn's children who were nonetheless members of the Royal House (as relatives of the reigning queen in the second degree of kinship and not excluded from the line of succession).
Sweden seems to be more consistent: currently all HRHs (including Princess Brigitta, who is not in the line of succession) are listed as members of the Royal House, whereas non-HRHs (including King Carl Gustaf's other sisters) are listed as members of the extended "Royal Family", but not of the "Royal House". Personally, I think that should be the right criteria.