I was born in one of those Commonwealth countries.
My ancestry is a mix of British and continental European.
I am proud of that heritage, and have a fair bit of regard for both sides of it.
However, I keep getting the impression that a lot of the stay at home British natives have an ingrained cultural belief that the citizens of those countries look to the UK in some preferential way, and perhaps for leadership or as a role model.
That is not necessarily true. In fact, despite apparent British faith in their superiority (not everyone, of course, but quite a few), many of us, particularly those with superior educations and an interest in history and culture, find British practices and social structures backward, undeveloped, and backward-looking. A hereditary aristocracy? Really? 'Class based' social stratification? Discrimination or social evaluation based on what school you went to, or your regional accent, or your religion?
Someone needs to drag the UK kicking and screaming into the 20th century, and then it can start working on catching up with the rest of us.
I have the option of establishing the right to live in the UK, or one of the continental EU nations. With the UK leaving the EU (along with its apparent desire to become an uber-surveillance state that would dumbfound Orwell), it's not going to be the UK.
It is entirely likely that most Commonwealth countries are not really interested in preferential ties to the UK as much as with other parts of the world, including the EU. You may make some headway with India and Pakistan if you liberalize immigration enough...