Queen Mary, Liverpool, Cardiff, Newcastle, Exeter, QUB, Southampton, Sheffield.
Then group LSE, UCL, KCL together as one entity (partial) UoL, let St Andrews in. This makes 15, a good number.
Make Durham, York, Nottingham, Glasgow, Leeds associate members. This makes 10.
Make Oxford, Cambridge, Imperial, London, Edinburgh core members. Termed it the 'Big Five'.