Regarding the effectiveness of native politicians and anti-colonial violence, it really varies a lot by colony. In several cases (e.g. British and Portuguese India and French Indochina) political and/or military pressure was indeed great enough that the colonial powers had to grant independence. However in the 1950s Britain defeated the two major colonial uprisings, in Malaya and Kenya, and some would say the same for France in Algeria (though this is debated and I couldn't judge personally). Also note that Portugal, a country with far less economic and military resources than Britain or France, managed to hold Angola and Mozambique quite successfully until the end of the military regime in 1974. Finally, the Soviet Union was able to defeat rebellions in Hungary and Czechoslovakia, and China retained control of Tibet and Xinjiang.

Part of it was economic. In 1956, due to the poor economic state it was in following the war, the UK wasn't ready to react to Nasser's nationalization of the Suez canal. It took months and a cooperative UK-FR force to get a sufficient force into Egypt.

The UN did not support the UK in the conflict and, to their surprise, the US didn't either. The world condemned the UK's actions, and UK-US relations were very strained. Until they had fully pulled out at the UN's insistence, Britain could not count on any economic aid from the United States. Cut off from Middle Eastern and American oil and with the Sterling's stability at risk, the UK was forced to pull out of the Suez without fulfilling their goal of taking over the Suez Canal (or their secondary goal of toppling Nasser).

After Suez, it was made clear that the United Kingdom was no longer a super power that could project its power as they could before WW2. They were junior partners in NATO, and they could no longer act without clear support from their friends across the Atlantic.

Source: Suez: "Britain's End of Empire in the Middle East" by Keith Kyle. Very good book, I'd highly recommend it.