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However, Mr English stressed there was no indication of a heightened threat in New Zealand and it was important to not let attacks such as that carried out in Manchester "paralyse ongoing public life''.
Soldiers will be deployed on Britain's streets to boost security as the country raised its terror threat to the highest level of "critical" following Monday's suicide attack that killed 22 people, including children, at US pop singer Ariana Grande's concert.
Police said they believed British-born Salman Abedi, aged 22, carried out Britain's deadliest bombing in nearly 12 years, and Prime Minister Theresa May said another attack could be imminent.
Today Mr English, Labour leader Andrew Little, Foreign Minister Gerry Brownlee, Justice Minister Amy Adams and Labour deputy Jacinda Ardern all signed the British High Commission's condolence book for the Manchester attack at Parliament.
Thousands of British tourists will soon arrive in New Zealand for the British and Irish Lions tour, with matches around the country from June 3 to July 8.
Auckland's Eden Park will host two of the Tests between the All Blacks and the Lions. The other Test will be held at Wellington's Westpac Stadium. Other matches will be played in Hamilton, Rotorua, Christchurch and Dunedin.
English said it was "disturbing'' that the UK terror threat had been raised to critical following the Manchester bombing.
There was no evidence of a heightened risk of attack in New Zealand, Mr English said, but intelligence agencies and other officials would remain vigilant.
On the Lions tour, English said New Zealand had experience hosting large events including the Rugby World Cup and Cricket World Cup.
"We have a team of people who are pretty experienced at it and I'm absolutely sure they will be taking into account these events, if only because so many of the fans coming here are coming from the UK.''
Asked if security at stadiums could be increased, English said that would be discussed in the coming days.
"I think one of the important aspects of how we deal with these incidents is to not allow them to paralyse ongoing public life.''
Mr English was yet to speak to Ms May, but had written to her this morning expressing support and condolences.
Mr Little said his written message today expressed the belief that "through solidarity and compassion we will get through these dark times''.
A terror attack could never be ruled out even in New Zealand, Mr Little said, and as such it was important to remain vigilant. However, he said such attacks were designed to both get attention and cause people to live in fear.
"The main thing is we make sure that people are safe... but we don't hold back on living life to the full.''
• The Lions take on the Highlanders at Forsyth Barr Stadium in Dunedin on June 13.