Newfoundland was offered the opportunity to become a dominion with the Statute of Westminster 1931. This would have given it free self-rule in its domestic matters, basically just leaving it allied and in a privileged trading position with the United Kingdom and the other dominions, which included Canada, Australia, New Zealand, and South Africa. A series of financial crises and near-bankruptcy caused Newfoundland to reject this arrangement, and its parliament requested that the British take up direct rule from London, which continued until it became a province of Canada in 1949.
Gibraltar has a unique governance structure, being officially a British Overseas Territory governed by a governor who reports directly to the British Crown. The UK government has responsibility for defense, external affairs and monetary policy, but the territory is self-governing internally and is an independent member of the EU.
Spain continues to claim sovereignty over Gibraltar, but a proposal in 2002 for the two nations to share sovereignty (an international arrangement known as condominium) was rejected by the voters of Gibraltar, with 98.48% of voters voting no.
There is a movement in Gibraltar politics to form closer ties with the UK, possibly by incorporating into the UK itself, which would mean Gibraltar electing representatives to the British parliament, but I won't go into that too much because of the 20-year rule (which I have already overstepped by talking about the 2002 referendum).
Only a couple colonies have given up/avoided offers of self rule, and all were due to economic and political turmoil. As already mentioned Newfoundland was one, but the Caribean colonies as well gave up self-rule.
White planters were given legislative assemblies of varying kinds in the early 19th century, however with the abolition of slavery and the crash of the sugar industry they gave up self-rule some 70 years later. London ruled the Caribean through unelected Govenors/commissioners until the 1940s-50s when varies nationlist movements that were separate from the planters arose.
I think it is worth noting that the Scots are one of the few members of the Empire who have been given a straight yes/no question on their participation. The overwhelming majority of colonies became independant through negotiations between London and representatives of some kind - be their nationalist movement leaders like Gandhi and Kenyatta, or Parliamentary leaders like John A MacDonald, Smutts, or Billy Hughes. Even the Irish, with their tradition of violent uprising negotiated the Anglo-Irish via a delegation from the Second Dail.
I can not think of a single commonwealth member that has become independant directly because of a referendum. (And I would apperciate help finding one)
Source: Canadian history undergrad, third year course in british history, stanley walports a new history of india.
Hi there! We're having a MEGATHREAD to corral all these types of questions, so I would ask everyone posting here to direct there attentions there. The rules are a bit more relaxed about the 20 years stuff.