Both in the British and American society the Hungarian revolution echoed, they reacted, those who thought Yalta was a mistake saw a chance to fix it.
On the level of actions however the governments of these powers had better things to do at places that they could reach more easily, and were more important for geopolitical reasons. So our struggle became a handy bait to distract the Soviet and gave time to secure the precious Canal from a perceived pro-Soviet threat in the Middle East - with the consent of the Soviet Union.
Consider this:
Egypt went from a candidate ally and client to enemy for the US in a couple of years perhaps less, but have to check the the chronology closer. They bought Russian weapons, recognized PRC, and nationalized the Canal. This was alarming. The threat that an enemy can cut off one of the most important sea lane on the world became a #1 item to solve on the problems list. When the SU is distracted elsewhere seems like the best time to fix this issue.
Since both French and British interests were harmed, surely they didn't need much encouragement to take matters in their hands. And since the US wasn't part of the action, Washington could step in as an outsider who wants to end the killing, legitimized by the United Nations and with it by the Soviet Union.
Sure, French and the Brits did not get back their "property", but the enemy lost a potential leverage too. The Canal was safe and sound, overseen by international participants.
With the very low cost of not doing anything about a Soviet client.