The Suez Canal was important to the British because of the fact that they had such a large overseas empire. By the time that the canal was built, the most important part of their empire was India. The Suez Canal made it much easier for them to transport goods to and from India.
Before the Suez Canal was built, it took much longer to transport goods to and from India. Ships making the trip had to go all the way around the southern tip of Africa which was, of course, much farther south than India. People could be transported more quickly as they could go through the Mediterranean and then travel by land to a port where they could take a ship for India, but that was not feasible for goods and was completely impossible for warships.
Because India was so important to the British economy, the canal was very beneficial. It allowed goods to get to and from India much more quickly and it made it easier to defend India. For this reason, the British were very eager to have control of the canal and the approaches to it.