HMS Spey will sail from Tahiti to Tonga carrying water and medical supplies.
Other supplies such as almost 100 tents are being sent on board HMAS Adelaide, of the Australian navy.
Liz Truss, foreign secretary, said: ‘Our thoughts are with those caught up in the appalling devastation and loss of life caused by the tsunami in Tonga.’
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UN humanitarian officials estimate that about 84,000 people — more than 80 per cent of Tonga’s population — have been affected by the eruption of an undersea volcano, which has led to deaths, injuries, loss of homes and polluted water.
The Hunga Tonga-Hunga Ha’apai volcano erupted on Saturday, triggering a tsunami which has caused devastation across the archipelago nation.
The defence secretary, Ben Wallace, instructed HMS Spey to sail to Tonga to assist in the humanitarian aid operation.
HMS Spey is due to arrive in Tonga next week and the vessel’s commanding officer, Commander Mike Proudman, said: ‘I’m proud that the Royal Navy can play its part in the efforts to respond to the devastating volcanic eruption and tsunami in Tonga.’
The United Kingdom has also offered to fund the deployment of crisis experts through the United Nations.
HMAS Adelaide will set sail on Friday carrying British aid including 90 family tents, eight community tents and six wheel barrows, with all items provided at the request of the Tongan government.