I think its a myth that Warwick is unknown outside of UK. They get plenty of research stduents from the worlds best Mathematics/Economics Schools and most people take international rankings with a pinch of salt.
In domestic rankings Warwick outranks UCL in every different league table (Guardian, CUG and Times) and most people when looking to apply to universities in a different countries look for domestic league tables and Warwick always appears in the top 10 for most subjects and in the top 4 for Maths/Economics/Business so most people will be aware of Warwick (heck they have 40% international students) this G5 group is as silly as russel group imo.
I believe it wont make a difference in your life if you go to LSE/Imperial/Warwick/Durham the only real elite universities are Oxford and Cambridge.