Why Is It That Citizens Of Common Wealth Countries Do Not Need Visas To Visit Them?

Commonwealth citizens born before 1 January 1983 may by virtue of having a parent born in the United Kingdom and Islands have the right of abode therein – such persons are exempt from all immigration control.....

Commonwealth citizens with a grandparent born in the United Kingdom and Islands may be admitted for up to five years on this basis, and thereafter be granted indefinite leave to remain.

Commonwealth citizens between the ages of 18 and 30 were eligible to be admitted for a "working holiday" for up to two years. 

This has since been replaced with the more restrictive Youth Mobility Scheme(now open only to youth of Australia, Canada, Japan, New Zealand, and Monaco).

Commonwealth citizens, unlike other non-European Economic Area nationals, may not be required to register with the police while living in the United Kingdom.