Having an air-carrier? How is that relevant to the question?
It's not quite the non-sequitur it looks like but it could do with a bit more context. Basically failure at Suez caused a major change in how the UK looked at themselves, or possibly recognition of the facts, and their position in the world. Success likely sees less retrenchment and a willingness to spend the money necessary to intervene in international affairs - hence forking out for shiny new carriers and the like.
To answer the question, the outcome is that Fr/Uk keep the Suez canal under important military control but give a more important profit share to Fuad II, the ''legitimate'' king of Egypt, who they put back on the throne in exchange of him closing his eye on the occupation.
This however is so wrong it's not even funny. This isn't about restoring colonialism or occupying Egypt for extended amounts of time, the Allies wanted to be in and out as quickly as possible. If the new leader or leaders stick to the 1954 treaty Nasser had signed and they don't try to unbalance the region the British and French would be more than satisfied with things.
In particular, since they were planning to remove Nasser who would they replace him with?
Something tells me that whoever serves as regent for young Faud, may pull a Sadat, and make nice with Israel 22 years early.
Faud? Yeah that's not going to happen, Farouk had made the monarchy simply too unpopular for any sort of restoration to be considered. It's going to be other members of the military that overthrow Nasser if it happens, if that occurs then, at least to begin with, I would see it going back to something more along the lines of the Revolutionary Command Council or similar collegiate system.
As long as they abide by the 1954 Anglo–Egyptian Treaty which had already agreed to a phased withdrawal of British troops, albeit with right of return in times of war, agreed to UN Peacekeepers in the Sinai to try and stop the low-level attacks across the border, and don't get pretensions of grandeur and try to become the next regional strongman the British won't care who comes out on top. Something which might well come back to haunt them later.