But the authority of these colonial legislatures in relation to Westminster was not always clear, especially as they ultimately derived their authority and even their existence from Parliamentary statute.
Initially, Parliament tried to resolve this problem through the Colonial Laws Validity Act of 1865. This laid down that colonial legislation was to have full effect within the colony itself, except for those laws which contradicted a statute of the UK Parliament which contained powers extending to that colony.
The law in effect confirmed the colonies' powers of self-government but that over-arching sovereignty was retained by the Westminster Parliament.
In 1931 Parliament developed a new relationship with the Dominions - a term first used in 1907 to describe the self-governing colonies - through the Statute of Westminster.
This Act repealed the Colonial Laws Validity Act and renounced the Westminster Parliament's right to legislate for the Dominions unless at their explicit request.
With the passage of the Statute of Westminster, the British Parliament conceded the last aspects of its authority over the Dominions to their own governments.
It marked the effective legislative independence of the Dominions from Britain and their equal status as nation states.
The Act initially applied to the six Dominions which existed in 1931 - Canada, Newfoundland, New Zealand, Australia, South Africa and the Irish Free State.
It was only formally ratified by Australia in 1942, by New Zealand in 1947 and was never endorsed by Newfoundland before that Dominion joined the Canadian confederation in 1949.
These Dominions (except for the Irish Free State, which became the Republic of Ireland in 1949) continue their links with the British Crown through the Commonwealth of Nations.
The Statute of Westminster is seen as the origin of the Commonwealth, the informal group of independent former British colonies which work together to promote democracy, human rights, good government and a number of other common values.