Rhodes Scholarships
They based their commonwealth on Ancient Greece. The Greek ideal was to create empire by culture.
To help achieve this they set up the 'Rhodes scholarships' to bring intelligent future leaders from around the commonwealth to Oxford to educate them according to the ideals of the group. Those trained at Oxford would form an elite technocratic class capable of spreading the British ideology to all corners of the empire and thus create a common governing mythology.
This mythology or grand narrative guiding society would be maintained by technocratic lobbying groups and think tanks such as the Royal Institute for International Affairs and the Council on Foreign Relations. These organizations would be the real locus of political power.