If you want to get into it, British dominance was built on a number of things (in no real order):
The Empire
Wealth
Industrial Prowess
Naval Hegemony
Britain was considered a Great Power up until the Suez Crisis in 1956, but by that point it was a holdover from the past. These key elements of Britain's power began to fade earlier. To deal with each of these factors:
Throughout the 1800s, Britain developed and maintained an enormous empire. Australia, New Zealand, Canada, South Africa - and the jewel of the Empire, India. These territories were complemented by the addition of vast African holdings in the 1880s and 1890s. But these territories were not content to remain territories.
Nationalist movements in Canada, Australia and New Zealand led the colonies to form united countries. At first, they were still directly controlled by the Empire under the dominion system. But with the seeds of self-identity planted, these countries became increasingly autonomous during the interwar period 1918-1939, taking control of their own foreign policy and increasingly assuming the mantle of independent governments. Why should these peoples be governed from Whitehall? Britain's importance faded as these countries came into their own.
Nationalist movements in India (Today split into India, Pakistan, Bangladesh and Myanmar) were even more intense. The Raj had remained relatively calm since the Sepoy Rebellion in the 1850s, but by the 1920s and 30s India was once again up in arms. Gandhi was the most prominent figure for independence in this period, leading a campaign of civil disobedience against the British authorities. Though Gandhi was eventually imprisoned, others took his place. India became increasingly difficult to govern - and both domestic and international support for the Raj waned. By the end of WWII, Britain was exchausted. It had neither the capacity nor the will to restore India fully to its rule - so independence was planned.
A wave of decolonisation followed in the 1950s. The increased emphasis on human rights after the war sparked a series of increasingly powerful de-colonial movements at home and overseas. International opinion turned against imperialism. Africa was let go to local governments in the 1950s and 60s - although the white minority governments that often clung to power in the transition faced a whole host of new problems. There were also arguably economic elements to this: national focus was on rebuilding domestically after the war - imperial holdings no longer brought the wealth or prestige that they once did. They became expensive overseas liabilities. Because of their reduced importance, there was less incentive to maintain them.
Secondly, Britain's power had traditionally stemmed from its enormous wealth - brought about by commerce (utilising the empire) and later its industrial dominance. Britain contributed relatively few troops against Napoleon - but for over a decade it bankrolled other nations' wars against him. This wealth exploded throughout the 1800s, enabling Britain to fund its empire - and the largest navy in the world to protect it. But WWI and WWII were of a new type of war ('total war'). Participants through everything they had against each other - and it was enormously expensive. Britain fell heavily into debt to finance both wars.
The Suez Crisis did not end because Britain could not compete with Egypt's army - it ended in part because Britain could not sustain the economic consequences. The US denied them loans through the IMF, and threatened to devalue the pound by dumping British debt on world markets. Other nations placed oil sanctions on Britain. Such an international response would have been unimaginable fifty or a hundred years earlier - not would it have had nearly the same impact. Britain could no longer afford to act unilaterally, and damn the consequences.
Thirdly, Britain was the heartland of the industrial revolution. Its enormous productive capacity and reputation for quality gave it a near-monopoly on many goods - and made it very wealthy. Britain was able to both bankroll and manufacture the equipment for wars. Its navy was the largest and most advanced in the world. When Russia was humiliated in the Crimean War (1853-1856), its ministers attributed Britain and France's successes to their industrial might - and they began a series of related reforms in Russia. Over the next few decades, Britain's relative importance diminished. Russia industrialised at a staggering rate. Japan grew even faster. But Germany and the US became true titans of industry, challenging and even eclipsing Britain. In this sense, Britain's power didn't diminish so much as that everyone else became more important.
But WWII changed that dynamic. British industry was devastated by the war. Rationing continued well into the 1950s. American industry, largely untouched by the war, boomed. European economies were desperately importing goods from the US to rebuild, and US companies were more than happy to comply.
The above two elements feed into the next one: British naval dominance. Throughout the 1800s, Britain maintained an informal policy that its navy should be the equal of the next two largest in the world, combined. This was formally adopted as policy in 1889. Britain's relative economic power had for decades allowed it to more or less achieve this goal. But by the 1890s - with the growth of Britain's competitors - it was no longer tenable. France and Russia bolstered their own navies in response. Germany engaged in an arms race with Britain to build dreadnoughts (the largest class of battleships). Japan and America became important sea powers - Japan's now impressive navy humiliating the Russians in the Battle of Tsushima in 1905. Britain was unable to maintain its naval hegemony throughout WWII - the Japanese devastated them in the Pacific, and the Royal Navy struggled for a time to respond to the threat of German U-Boats in the North Sea and the Atlantic. Again, in the devastation after WWII, Britain was simply not able to maintain its large navy - the fleets were quickly disbanded, and Britain ceased in part to be a dominant sea power. They instead began to rely on the US for naval protection under the NATO umbrella.
Ironically, the naval hegemony cementing Britain's primacy proved to be less important than anyone had expected. Britain's armies were traditionally smaller than those of other continental powers, so this was damning. Many believed navies would play a vital part in the First World War - in the preceding years, most countries put significant resources into bolstering their navies - the aforementioned 'dreadnought race' was one example. But after all that, there was one major sea battle in WWI - the Battle of Jutland. The Germans won, but realised that they could not sustain losses at the same rate the RN could - so they stayed bottled up for the rest of the war. The conflict was decided on land, where Britain's contributions - though still very impressive - were not the undeniable force they were on the sea.
TL;DR: Britain's importance diminished as its rivals grew. France, Russia, Japan, Italy - and the big two, Germany and the US - all became more powerful throughout the 1800s and early 1900s, at Britain's expense. WWI and WWII drained the empire, sapping at its population, wealth, and industrial might. Nationalist movements across the Empire grew, rewarding independence to previously subject lands. The Suez Crisis was only the final nail in the coffin - it proved that Britain (and France) could no longer run roughshod over other states, as they had done in the past. Britain shrank into the role of "lesser partner" to the US.
Palestine, Iraq, Kenya, and Papua New Guinea did not bankrupt or destroy the empire. They were prizes acquired by Britain at the end of the first world war. They were acquired during a period that was already tenuous period for the empire. Britain's relative importance had been falling for decades, and nationalist movements were making serious gains - although without WWII it is difficult to say what might have happened next.