The family of a Christchurch man stabbed in the London Bridge terror attack says he's doing okay.

Oliver Dowling was out for dinner with his girlfriend at the Borough Markets on Saturday night local time when the attack happened, leaving seven people dead.

The 32-year-old is one of 48 people that were injured, being stabbed in the face, neck and stomach. 

He has woken from an induced coma and his parents and older brother are with him.

They've thanked staff at the University of London Hospital for their tireless efforts over the weekend.

The condition of Dowling's girlfriend Marie is still described as very serious.

Her family have flown from France to be at her bedside.

British Police say they know all of the attackers and two of the men have been revealed.

They've been named as Khuram Shazad Butt, and Rachid Redouane. Both from east London.

Khuram Shazad Butt was British born, while the other man claimed to be Moroccan and Libyan.

British Prime Minister Theresa May says officials are working hard to identify all the victims.

"It is now clear that sadly, victims came from a number of nationalities. This was an attack on London and the United Kingdom but it was also an attack on the free world."

At a vigil, London Mayor Sadiq Khan told the crowd the city stands in defiance against the attack.

"I want to send a clear message to the sick and evil extremists who commit these hideous crimes. We will defeat you. You will not win.

"Your perverse ideology has nothing to do with the true values of Islam and you will never succeed in dividing our city."

Donald Trump's stepping up his criticism of London's mayor and how he handled the attack aftermath.

At least 7 dead and 48 wounded in terror attack and Mayor of London says there is "no reason to be alarmed!"

— Donald J. Trump (@realDonaldTrump) June 4, 2017

But Mr Khan isn't fazed.

"Look can I just say this, my focus from Saturday night has been working with the police, emergency services and the government to deal with the horrific attack on Saturday. I just haven't got time to respond to a tweet from Donald Trump."

Theresa May's leaping to Khan's defence, saying she doesn't agree with Mr Trump, but has stopped short of condemning him.