"Words will never be able to match his essence. There will only ever be one James. Nowhere else will you find such humour. He was an inspiration," she said, adding that the police would be unable to formally identify him until the coroner's report tomorrow.
McMullan had not been seen since he stepped outside a pub for a cigarette on to London Bridge near where the van was later seen to have crashed.
Earlier, Melissa McMullan had pleaded for his safe return, saying: His family need him home x."
He is the second victim to be named after Canadian woman Christine Archibald who died on London Bridge. Five people remain missing with family and friends leaving desperate pleas on social media to help find them.
Spaniard Ignacio Echeverria, 39, has not been seen since he ran to help defend an injured woman and took on the attackers with his skateboard.
His brother Joaquin said the family had been asked to provide his fingerprints and fear the worst for him.
Friends and family of a Brisbane woman, Sara Zelanak, 21, have also posted about fears for her safety, saying she became separated from friends and has not been seen since.
Her heartbroken stepfather Mark Wallace said his family hadn't heard from her for 48 hours and authorities hadn't been able to shed any light on where she was.
Prime Minister Malcolm Turnbull said he believed four Australians were caught up in the attack. Two of them, including Zelanak, remain unaccounted for after Candice Hedge and Andrew Morrison were found to be recovering from serious injuries.
Frenchman Sebastian Belanger has also not been seen since Saturday. His girlfriend Gerada has launched appeals online asking "if anyone has seen him or knows anything contact me".
Another Frenchman, Xavier Thomas, also remains missing. His girlfriend, Christine Delcros, is in hospital and her sister shared a post on Facebook asking for help to find them.
"We're en route to London, my sister Christine Delcros and her boyfriend Xavier Thomas have been victims of the #attack #London #londonattack on the #londonbridge. My sister is seriously injured and hospitalised
"I appeal to all those who have news of #Xavier #Thomas who is missing ... We're terribly worried ..." she said.
Another young man, Socaine Drz, has been named by family as missing. His aunty, Hatice Bodur, shared a photo of him and asked friends to get in contact if they have seen him, the Sun reports.
"If you see this Socaine please return home. We are worried sick police are looking as well."
On Monday UK Prime Minister Theresa May said the "victims came from a number of nationalities" and it would take some time for authorities to contact the next of kin.
"This was an attack on London and the UK but it was also an attack on the free world," she said.
BROKEN INTO 'A MILLION PIECES'
The family of the Canadian woman named as the first victim have revealed her fiance's heartbreak as he tried to perform CPR on her.
Christine Archibald, 30, was hit by the speeding van on London Bridge. She had been out for a late-night walk to see the sights of London having visited the capital from the Netherlands with her fiance, Tyler Ferguson.
Ferguson's sister said she spoke to her brother on the phone after the attack and urged friends to help support him after his heart had been broken into a "million pieces".
"Last night in London, my baby brother, lost the love of his life on the London Bridge," she said.
"In a split second his entire life was ripped away from him. Hearing his painful sobs on the phone while he's alone trying to deal with this tears me apart.
"I have no words. If you know Tyler, please be there for him now, and later when what happened sinks in, he's going to need us all."
Ferguson's brother Mark told a British Columbia news station that the pair were in London for a week from The Hague where Ferguson works as an accountant. Archibald decided to join him on a work trip.
"She had never been there before so they decided to take a walking tour of London in the night-time," he said.
"He was showing her some sights and walking around and just enjoying the nice night."