New Zealand will get the help of a UK search-and-rescue team which has been deployed to join the relief effort after the Christchurch earthquake, David Cameron has said.

The British prime minister sent his “deepest sympathies” on behalf of the UK, to New Zealand after the deaths of at least 65 people in the earthquake at 12.51 on Tuesday (2351 GMT on Monday).

He said the UK “stood ready” to help more at this “dark and difficult time”.

During a visit to Kuwait, Cameron said: “There are many people in Britain with ties of friendship or family to New Zealand.

“They will be following events particularly closely and with understandable anxiety.

“I believe I speak on behalf of everyone in our country when I say that we all stand with New Zealand at this moment, at this dark and difficult time.”

A state of emergency has been declared in Christchurch and the authorities are warning the death toll is likely to rise.

Emergency teams are now working under floodlights to reach survivors, as relatives keep vigil outside.

The airport is closed, many power and telephone lines have been knocked out, and burst water mains have flooded whole districts.

The Foreign Office said it was “urgently” seeking information about possible British casualties from the earthquake.

Cameron said the UK’s high commissioner in the country was on her way to Christchurch, and extra consular staff would arrive on Tuesday.

“The people of New Zealand have been hit by a devastating earthquake, not once, but twice in a matter of months, and I want to pay tribute to their resilience,” he said.

The UK rescue team dispatched to New Zealand consisted of 62 people and more than nine tonnes of equipment.

They will arrive in New Zealand on Thursday to provide relief for teams already on the ground.

“It is a long way from the UK to New Zealand and so our team will take a while to get there, but the New Zealand government confirm that assistance is very much required,” the Foreign Office said.

The earthquake hit Christchurch just as it was still trying to recover from a 7.1-magnitude tremor in September, which left two people seriously injured but no fatalities. It caused an estimated $3bn (£1.9bn) in damage.

Although stronger, the previous quake happened in the middle of the night and its epicentre was further away and deeper underground.

New Zealand sits on the Pacific Ring of Fire, a vast area of seismic activity, and records more than 14,000 earthquakes a year, although only about 150 are felt by residents.

Christchurch is home to almost 400,000 people, and is considered a tourist centre and gateway to the South Island.

The Queen has delivered a message of support to New Zealand Prime Minister John Key. She said: “Please convey my deep sympathy to the families and friends of those who have been killed; my thoughts are with all those who have been affected by this dreadful event.

“My thoughts are also with the emergency services and everyone who is assisting in the rescue efforts.”

Barnaby Luck, from Haverford west in Pembrokeshire, was in a hostel when the disaster hit.

The 29-year-old, who has been travelling through New Zealand since November, said: “It was like someone had got hold of the building and was shaking it back and forwards, so I just jumped under my bunk bed.

“The house was picked up like something from The Wizard of Oz and shaken for what seemed like a minute.”

Backpacker Christopher Ratcliffe, 27, from Sutton Coldfield, West Midlands, was forced to shelter under a desk in a library.

“When I came outside the city looked like a bomb had hit it,” he said.

“There was dust and smoke in the air and bits of glass and rubble falling from the tops of buildings. People were walking around covered in blood and in tears – it was just shocking.”

The New Zealand High Commission in London is advising New Zealanders in the UK who are worried about friends and family to monitor the government’s official websites, media reports and to try to make direct contact.

It also advised those due to travel to Christchurch to contact their airline or travel agent. All other South Island and New Zealand airports are open.

The latest information can be found on the Ministry of Civil Defence and the Environment Canterbury website.

New Zealanders in the UK who are worried about family and friends should continue to monitor the above websites, media reports and try to make direct contact.

Once a national helpline has been established that number will be provided via the websites above.

British nationals concerned for British family and friends in New Zealand should contact the Foreign and Commonwealth Office for consular advice

The Ministry of Civil Defence are asking that in order to minimise loading on the telecommunications network, people use text messaging to check if family and friends are safe.