Rather than the Russell Group or the Sutton Trust 13, I personally believe that the Golden Triangle feels more like the Ivy League.
Just as the Ivy League does not denote all the best unis in the states, Golden Triangle does not represent all the best unis in the uk. I personally regard Golden Triangle similar to the Ivy League in terms of several different aspects.
The fact that both of them are focused on distinct and specific regions also make the Golden Triangle similar to the Ivy League. For that reason, Golden Trinalge does not include Warwick, Durham, Bristol, Nottingham and York. And the Ivy League does not include Stanford, Duke, MIT, Caltech, Berkeley, Chicago, UCLA, Texas at Austin, etc, despite their excellence and prestige.
Golden Triangle = orginally best research universities in the uk. nowadays, it is more known globally as the most prestigious universities in the UK within London and near London. (around London)
Ivy League = originally a sports league among unis in the north eastern part of the states. nowadays, it denotes social elitism and the most prestigious universities in the north eastern part of the states, in the eyes of the public.
Plus, they are similar considering the number of unis within each group. Well, the Ivy League has more unis, but that's because the US is much bigger than the UK and thus has more prestigious unis. Some people could argue that 6 members is still too much for a British group, but Britain has longer history of excellent higher education than the US does.
Ivy League: 8 members
Harvard
Princeton
Yale
Cornell
Columbia
Brown
Dartmouth
Pennsylvania
Golden Triangle: 6 members
Oxford
Cambridge
University College London
King's College London
Imperial College London
London School of Economics.
Furthermore, both groups have a few members who are not as much recognized as the others in the group. For the Ivy League ones, those not as recognized are Dartmouth and Brown. For the Golden Triangle, one member who is not as recognized by the general public is King's College London. (no wonder why king's ranks similarly to brown on almost all world rankings)
Russell group can't be anywhere close to the Ivy League, because it has too many universities within it, the level of prestige among its members vary too much and the members are located everywhere in Britain. (and not just 'around London' or 'in Scotland', etc)
The Sutton Trust 13 isn't like the Ivy League as well, with the reasons being similar to the ones I gave for the Russell group. It's closer than the Russell group though, since the level of academic excellence and prestige among its members varies less, compared to the Russell group. However, the fact that it is also meant to be a set of the best universities in the UK that provides more oppurtunities for the underprivileged students makes it very different from the Ivy League, which is known for being more accessible to upper classes and 'preppies'. (hence, a symbol of social elitism.)