Suez was won tactically and lost at the political center of gravity

What additional capability would Britain have needed to force a military solution during the Suez Crisis?

Not more battlefield power; it needed far greater political influence within the Egyptian military and a viable postwar settlement.

British, French, and Israeli forces rapidly overmatched an Egyptian military still in transition. The campaign was a military success but an economic and political failure. A durable outcome required Egyptian officers to turn against their own leadership in a way that could remain acceptable to the United States. Britain overestimated its influence and working relationships inside the Egyptian military, so additional ships or aircraft would not address the real center of gravity.