Britain made two major contributions to the war against Japan in 1944-45. The first was the Burmese campaign, which had been Britain's main contribution since 1941, while the second was the British Pacific Fleet, which are the carriers you mention.

Until 1945, the Royal Navy confined its operations to the Indian Ocean. During 1944, it began to build up strength in the region, in preparation for a move to the Pacific. In the latter half of 1944, these forces carried out several raids on targets in Indonesia. These began with Operation Cockpit, an attack on the naval base at Sabang, in May 1944, which was carried out by USS Saratoga and HMS Illustrious. Later operations were carried out solely by British carriers. Until 22nd November 1944, Royal Naval forces in the Indian Ocean came under the Eastern Fleet. On the 22nd, the British Pacific Fleet (BPF) formed, and took control of the carrier forces, as well as several modern battleships. In January 1945, the fleet redeployed to Sydney. While in transit, it took the chance to attack the oil refineries at Palembang, on Sumatra. Most of February was spent working up and replenishing aircraft in Sydney. In March, the BPF began operations alongside the US 5th Fleet as Task Force 57. It's first operation was as part of the covering force for the Battle of Okinawa. The BPF had the job of suppressing the airfields on the Sakishima Islands to prevent kamikaze aircraft from staging from these islands. As the British carriers were more heavily armoured, and thus more survivable against kamikazes, they were also used to suppress the airfields on Taiwan, as it was believed that the most effective kamikaze units were based here. During July 1945, the BPF operated against the main Japanese islands in conjunction with the US 3rd Fleet, operating as TF37. These operations consisted of attacks against airfields, military installations and shipping, including the escort carrier Shimane Maru, the only carrier attacked by the RN in WW2. Transport links were also attacked. Royal Navy submarines also made contributions to the war, primarily from bases in the Indian Ocean. Operation Struggle, the attack on Singapore by two midget submarines, is worth looking up. The RN contribution was perhaps not the most significant, but it taught important lessons in international cooperation and fleet operations.

The main British Army contribution was the Burma Campaign. This had started in January 1942, with the Japanese invading Burma. British and Empire forces were forced to retreat northwards. Eventually, the front line stabilised along a line running roughly north-east from the Arakan province on the coast to the Chinese border. During the remainder of 1942 and 1943, the front line didn't really move. Neither side could commit a decisive force, due to commitments elsewhere. In early 1944, this changed. The Japanese attempted a major invasion of India, masked by a diversionary attack in the Arakan. The diversionary attack was unsuccessful, while the invasion of India was defeated at Imphal and Kohima. This was probably the Japanese army's most significant defeat until the Russian invasion of Manchuria, with 60,000 dead and over 100,000 wounded. Operations in the latter half of 1944 consisted mostly of pursuing the retreating Japanese forces. Amphibious landings were made to cut off Japanese troops using the coastal road. In March 1945, a Japanese counter-attack attempted to recapture the town of Mektila. This was defeated with heavy casualties. With the aid of an anti-Japanese uprising, the Allied troops made quick advances towards the major port of Rangoon, but were held up until 30th April by strong resistance at Pegu. This allowed the Japanese to evacuate before Operation Dracula, an amphibious attack on Rangoon, took place. The last battle in Burma was the Sittang Bend Battle. Japanese troops inland had been cut off by the Allied advance. These troops, covered by a diversionary attack, attempted to break out. The diversionary attack went in early, and was defeated. Stripped of their covering attack, the attempted breakout was a disaster, with troops falling into ambushes, or drowning crossing monsoon-swollen rivers. Had the atom bombs not been dropped, the next step would have been Operation Zipper, an amphibious assault on the Malaysian Peninsula.

The RAF mostly operated in support of the British Army in Burma. They made several strategic bombing raids on targets in South East Asia, particularly Singapore. The war ended before the main RAF contribution was ready. This was Tiger Force, a twenty-two squadron strategic bombing force. Operating mainly Avro Lancasters and Lincolns, it would have operated from Okinawa in support of the American strategic bombing offensive. This force consisted of some of the most experienced squadrons of RAF's Bomber Command, including 9 Squadron, which sank the Tirpitz, and 617 Squadron, of Dambusters fame.

While not technically British, but falling under their command, ANZAC troops made a strong contribution to the Pacific Theatre. In late 1944 and 1945, they were mainly concerned with mopping up the Japanese presence in Papua New Guinea, and the recapture of much of the Dutch East Indies, particularly Borneo.

For more information on the BPF, I'd recommend this article. Max Hasting's Nemesis is a good introduction to the later part of the Pacific Theatre, and is quite detailed on Burma.

NB — British contribution, not English. It seems like pedantry, until you're talking to a Welshman, a Northern Irishman or a Scot (like me!)

Britain's role in the Pacific tends to get somewhat overlooked — partly because the theatre was dominated by the US, and partly because the popular memory of Britain's war is largely fixated on the European theatre and the Churchill vs Hitler paradigm.

So, to put the 1944-1945 situation in its historical context:

The British and their colonial allies were heavily engaged in the Pacific right from the get-go until July 1945: the Japanese launched attacks on British possessions in the Far East almost simultaneously with the raid on Pearl Harbor — Hong Kong and British Malaya were attacked on 8 December 1941, and 'Fortress Singapore' came under siege in February 1942.

Britain's major regional interest was India — the cornerstone of the British Empire — but also the potential vulnerability of Australia and New Zealand if Japanese expansionism went unchecked. Indian troops were a major component of British forces in southeast Asia.

The US island-hopping campaign and the long, hard push towards mainland Japan represented one major sub-front in the Pacific Theatre — meanwhile, British Commonwealth forces were fighting a difficult jungle war in continental southeast Asia (the China Burma India Theatre.)

The Burma Campaign was Britain's longest of the war, and cycled through multiple failed offensives and stalemates; the real fear was that Japan would mount a more substantial invasion of the Indian subcontinent. The Japanese even sponsored a small corps of Indian nationalists (the Indian National Army) whose objective was to liberate India from British rule.

Now, to answer your actual question:

In spring of 1944, the Japanese launched the U-Go offensive (one of their last), invading northeast India. The offensive was decisively broken by a major Japanese defeat at the battles of Imphal and Kohima — two of the worst military setbacks the Japanese suffered during the war. In response, Britain launched a series of counteroffensives in mid- and late 1944, driving deep into occupied Burma with the ultimate objective of recapturing Rangoon.

In January and February 1945, the British forces broke the back of Japanese forces in Burma at the Battle of Meiktila and Mandalay; at this point, the Japanese were fighting (and losing) on at least three fronts: the Chinese were pushing them further and further back, and US forces were closing in on Okinawa.

In May, the British launched a combined amphibious/airborne attack (Operation Dracula) on Rangoon — though by that point, the Japanese were already in retreat across the region. Aside from an attempted breakout by encircled Japanese forces at the Battle of the Sittang Bend, the campaign in Burma was all but over, and preparations were underway for an invasion of occupied Malaya when the atomic bombs fell.

So the tl;dr is that Britain was heavily involved in the Pacific — just not in the bits which have lodged in the popular memory; the British 14th Army is often referred to as the 'Forgotten Army' for that reason. I'd suggest looking at Louis Allen's Burma: The Longest War or Christopher Bayly and Tim Harper's Forgotten Armies. The Fall of British Asia 1941-45.