The Suez Canal came about very late in the game as far as the British Empire was concerned. It was constructed and owned by a British/French/Egyptian multinational consortium and completed in 1869. It was not directly controlled by the British until the occupation of Egypt in 1882 and even then the Suez Canal company was, to my knowledge, still majority French owned.

Its strategic importance is in the fact that it essentially cut the travel time from India or the far east to Britain roughly in half. By the time of the first World War it was also the primary supply route for Persian Gulf oil, on which the British navy depended. So by 1914 I think you can see the vital strategic importance which is that for a country that relied on its navy, control of the canal meant control of the oil, without which the navy couldn't function. The result was that the Ottoman raids on the canal forced the British to deploy large numbers of troops to defend the canal.

The canal was also eventually quite profitable, particularly as shipments of oil became more common. Historically the canal has accounted for about a quarter of the revenue of the Egyptian government after the canal was nationalized.

It was was of great symbolic importance. More so even then the territory in the empire, "Suez" or "East of Suez" came to be synonymous with the empire itself. The latter phrase used in Rudyard Kipling's poem Mandalay:

Ship me somewheres east of Suez, where the best is like the worst,

Where there aren't no Ten Commandments an' a man can raise a thirst;

For the temple-bells are callin', an' it's there that I would be --

By the old Moulmein Pagoda, looking lazy at the sea;

On the road to Mandalay,

Where the old Flotilla lay,

With our sick beneath the awnings when we went to Mandalay!

On the road to Mandalay,

Where the flyin'-fishes play,

An' the dawn comes up like thunder outer China 'crost the Bay!

And the same phrase was used by Harold Wilson in 1970 in what essentially signaled the final "end of empire" when he announced that Britain was withdrawing its military bases and protectorates back from east of Suez, with the exception of Hong Kong. (I think he may have technically used the phrase "East of Aden" but Suez is what stuck.)

Even more so I think than the loss of India, the loss of Suez was unconscionable in the minds of many British politicians which in turn resulted in the Suez Crisis after Nasser seized the canal, which was the last area of Egyptian independence that had not been ceded to the them. The Americans were incredulous at this reaction, as they didn't understand why Britain would conspire to defend a canal that went to an empire they no longer had.

So yes, Suez was both of vital strategic importance, particularly after the conversion of the British navy to oil under Churchill, as well as of great importance in the British consciousness of their role in the world, even after they had lost control of the canal itself.