The Philippine government raised the official death toll to 1,744 on Tuesday, but the figure is expected to climb drastically, with authorities estimating that the storm killed 10,000 or more across a vast region of the country, and displaced about 660,000 others.
David Cameron said HMS Daring, which carries equipment to make drinking water from seawater, would provide humanitarian assistance and flights from its onboard helicopter. At least one Boeing C-17 military transport aircraft would be allocated to move humanitarian aid to areas that are most in need and hardest to reach, the prime minister said.
"HMS Daring, currently deployed near Singapore, will shortly be heading at full speed towards the disaster zone with further support from an RAF C-17 which will be a powerful help to the relief operation," Cameron told a dinner attended by business leaders in London.
HMS Daring is expected to reach the area in five days and the C-17 within the next few days. About 200 military personnel will be involved.
Britain has swiftly ratcheted up its response to the devastating typhoon Haiyan, bringing its contribution since the disaster struck to £10m.
Britain's Department for International Development on Saturday pledged an initial £6m to help get food, shelter and clean water to people in need.
The United States is sending the USS George Washington aircraft carrier and other ships, US officials said on Monday.
The Pentagon said defence secretary Chuck Hagel had ordered the nuclear-power aircraft carrier and other ships "to make best speed for the Republic of the Philippines".
The George Washington is now in Hong Kong and was expected to arrive within 48 to 72 hours, along with other ships, including guided missile cruisers and destroyers. Crew were being recalled early from shore leave, the Pentagon said.
With some 5,000 sailors and more than 80 aircraft, the George Washington brings enormous capacity to relief efforts.
Beyond serving as a staging platform for flights, the carrier's water distilling plants can produce 400,000 gallons of fresh water a day, according to its website.
"As needed, these ships and aircraft will be able to provide humanitarian assistance, supplies and medical care in support of the ongoing efforts," Pentagon spokesman George Little said.
At least a dozen US and Philippines military cargo planes arrived in Tacloban on Monday, with the Philippine air force saying it had flown in about 66 tons of relief supplies since Saturday, but poor weather hampered a resumption of flights on Tuesday morning.
An initial contingent of US forces is already on the ground, with most operating out of Villamor Air Base in Manila, and a smaller group in Tacloban.
Accompanying the George Washington will be the cruisers USS Antietam and USS Cowpens and the destroyer USS Mustin.
The supply ship USNS Charles Drew is already under way and will rendezvous with the group as they get closer, the Pentagon said. The destroyer USS Lassen had also left for the region, officials said.
The George Washington also counts a carrier air wing on board with helicopters that can bolster disaster relief efforts, if required, officials said.
Among contributions from other countries, Australia announced a $A10m (£5.8m) package, including medical personnel and non-food items such as tarpaulins, sleeping mats, mosquito nets, water containers and hygiene kits. New Zealand will give NZ$2.15 million (£1.1m) in aid.
Japan is to send a 25-strong emergency medical relief team, Indonesia is to dispatch aircraft and logistical aid including personnel, drinking water, food, generators, antibiotics and other medication.
The European Commission said it would provide €8m (£6.7m) to help worst-affected areas. The Chinese government is providing $100,000 and the Chinese Red Cross a further $100,000. The Vatican pledged €3m.
Comment: The US.-UK regime has some nerve posturing as the Philippines' saviour. Having colonized and indirectly (and sometimes very directly) militarily occupied the country for over 100 years, the Anglo-Saxon elites are substantially to blame for Philippines never developing adequate infrastructure to cope with typhoons and everything else Nature throws at it.