Britain was a naval power, and in the early 20th century was rich in several factors that served as a basis for that, including iron and coal, as well as access (through trade) to the essentials of munitions manufacture (saltpetre, an ingredient in gunpowder and other propellants, was abundant in India).
But coal-fired ships were cumbersome to manage: solid coal had to be physically handled when fueling ships initially, in re-bunkering coal as it was consumed in transit, and of course, being shoveled into the boilers themselves.
Petroleum, by contrast, flowed through pipes, by gravity or with the assistance of pumps. Fueling, bunkering, and operational procedures were streamlined remarkably. Ships also gained vastly greater performance flexibility: direct-combustion engines (diesel or turbine) could be powered up or down in seconds, rather than the many minutes or hours to increase steam-based output. And of course petroleum enabled the two great 20th century advances in naval power: submarines and aircraft, of which the technological history of coal-fired variants is brief.
(Not non-existant, however. The British Navy deployed K-Class submarines, coal powered, in WWI, and the Germans experimented with a coal-dust burning airplane in WWII, see <https://en.wikipedia.org/wiki/British_K-class_submarine> and <https://en.wikipedia.org/wiki/Lippisch_P.13a>.)
Britain's problem in 1913 however was that the country had no domestic oil production capacity. (The North Sea oil fields wouldn't be proven and developed until the 1960s.) Switching from (domestic) coal to (foreign) oil was a tremendous gamble, and required sea-lane control to the Middle East, as well as control of the Suez Canal for greatly-reduced shipping costs.
The story of oil in both World Wars is probably the most fascinating aspect of Yergin's book. WWI in particular started with cavalry charges and horsecarts, and ended with tanks, submarines, and bombers. During WWII, a critical element in the Allied invasion of mainland Europe was the establishment of an oil pipeline, in Operation Pluto, initially consisting of a single two inch diameter cross-channel pipe. Through those two inches flowed the material which made mechanised invasion possible.
<https://en.wikipedia.org/wiki/Operation_Pluto>
(Appropriation of German "Jerry Cans" --- Wehrmacht-Einheitskanister to its creators --- was also a huge strategic gain. <https://en.wikipedia.org/wiki/Jerrycan>)