Britain has warned of severe consequences after US and UK warships repelled a barrage of 20 Houthi rockets, drones and cruise missiles fired at ships in the Red Sea.

It was the most sustained and complex assault by the Iranian-backed group since the Houthi force governing Yemen from the capital, Sana’a, launched its attacks.

There have been than 20 attacks since mid-October, deterring a large number of shipping companies from using the Red Sea naval route and pushing up prices.

Grant Shapps, the UK defence secretary, said: “The attacks launched by the Houthis are unacceptable and their consequences will be severe.”

A UN security council resolution condemning the Houthi actions, but not authorising the use of force, is due to be passed in New York on Wednesday. It is unclear whether any other country, particularly France, will be willing to join what could be joint US-UK reprisals against the Houthis.

A military spokesperson for the Houthis, once seen as a minor localised military force, said in a statement the attacks would continue “until the siege of Gaza is lifted”.

American and British forces said they shot down 18 drones and three missiles on Tuesday. “Iranian-backed Houthis launched a complex attack of Iranian designed one-way attack UAVs … anti-ship cruise missiles, and an anti-ship ballistic missile from Houthi-controlled areas of Yemen into the southern Red Sea,” the US Central Command (Centcom) said.

The drones and missiles were downed by a combination of F/A-18 warplanes operating from the USS Dwight D Eisenhower aircraft carrier and one British and three American destroyers, Centcom said, adding that there were no injuries or damage reported.

The US set up a multinational naval taskforce last month to protect Red Sea shipping from Houthi attacks, which are endangering a transit route that carries up to 12% of global trade.

Shapps said the HMS Diamond “repelled the largest attack by the Iranian-backed Houthis in the Red Sea to date”. He added that the ship, described by the Royal Navy as “a jewel in the naval crown”, destroyed multiple attack drones with guns and Sea Viper missiles.

The US said no Iranian ships were involved in the attack.

Last week, 12 countries led by the US warned the Houthis there would be direct consequences if the attacks undermining freedom of navigation along the busiest waterways in the world were not brought to an end.

The Houthis formally rejected the western demand in a letter to the UN, and followed this up with a military assault that reduced the options available to Centcom.

Plans to designate the Houthis as a foreign terrorist organisation, a designation lifted by the US president, Joe Biden, at the start of his term in office, have fallen away as an alternative response.

The Houthi military spokesperson said: “We carried out an operation with a large number of ballistic and naval missiles and drones targeting an American ship that was providing support [to Israel]. The operation came as a preliminary response to the treacherous attack on our naval forces by the American enemy.”

He added: “The Yemeni armed forces continue to prevent Israeli ships or those heading to the ports of occupied Palestine from navigating in the Arab and Red Seas until the aggression stops and the siege on our steadfast brothers in the Gaza Strip is lifted. The Yemeni armed forces confirm their full commitment to the continuation of shipping traffic in the Red and Arabian Seas to all destinations except the ports of occupied Palestine.”

Western officials are discussing which countries might be prepared to be part of military action against Yemen, with most attention focused one whether French ships would join an attack on coastal radars.

One issue under discussion is whether the US would mount a single punitive attack or a longer-term campaign to identify the mobile sites from which Houthis are firing missiles.

Whitehall estimates based on shipping industry forecasts suggest the global impact of extended disruption to shipping could lead to a 0.2-0.5% rise in inflation, with the impact most severe on the finances of Egypt due to the loss of commercial shipping through the Suez canal.

The UK has long been convinced that Iran is arming and training the Houthis but says the Houthis are not taking this action on the instruction of Tehran.

Privately, Saudi Arabia and the United Arab Emirates, two countries that have battled with the Houthis in the nine-year Yemen civil war, are said to be sympathetic to military action against the Houthis but are wary of being seen to support US-led military action against a group that has won extensive popular support for its acts of solidarity with Gaza.