They did so for no strategically valid reason.

From Small Wars, Faraway Places by Michael Burleigh. Page 284.

Before the Suez Crisis in 1956 the British were confident that they were still one of the great powers in the world. Afterwards the more realistic of them grasped that this was no longer so. At the eye of the ensuing storm was Anthony Eden, whose mental and physical ruination symbolized the burdens that Britain could no longer bear. The crisis involved oil, complex legal issues about ownership, and the wider strategic architecture of the Middle East.

The Suez Canal was operated by an Anglo–French company whose commercial concession would expire in 1968. Around 122 million tons of cargo passed along the Canal each year, 40 per cent of it oil, which included two-thirds of Western Europe’s oil supplies; in contrast, only 5 per cent of US oil imports went through Suez. In the early 1950s the Egyptian government received just $3 million of the company’s annual profits of $100 million, a source of burning resentment to the Egyptian ruling elite.

Britain controlled an area the size of Wales on either side of the Canal, in which it stationed 80,000 troops, a legacy of its armed intervention against the Egyptian military uprising of Ahmad Urabi in the 1880s. Potentially, this force could be used to determine who ruled in Cairo, though by the early 1950s it was just another brick in the global containment of the Soviets. The 1936 treaty governing this last arrangement was renegotiated in 1953–4, with the British agreeing in October 1954 to withdraw their troops within twenty months. By that time it had been decided by defence experts that the Soviets could be contained elsewhere. So when the British and their allies returned in force by air and sea in November 1956, they did so for no strategically valid reason.

Having lived intermittently in England from the 1960s through the 1980s, it is hard to communicate to Americans how shocking was the Suez Crisis to the British public. That it should happen at all and then that it should fail.

In the US I suspect it would be hard to find anyone outside of history departments in some universities who would even be able to recognize the Suez Crisis, much less explicate it. Yet, in Britain, it remains a persistent scar in the world view of the Mandarin Class.