May and Turnbull earlier visited the Borough Market where two Australians were killed in last month's terror attack that killed 11 people.
Mr Kennett said he had written a "laudatory" article praising Mr Turnbull's performance in his European trip but he was now in despair.
Mr Kennett said he did not agree with all of Mr Abbott's policy positions but that Mr Turnbull should have appointed the former prime minister to his cabinet.
He fought back tears as he heard stories from survivors and spoke about how Sara Zelenak and Kirsty Boden had tried to fight off their attackers.
Ms May later welcomed Mr Turnbull to Downing Street for talks, including plans to work more closely together on national security matters.
May said the topic came up during the recent G20 summit held in Hamburg, Germany and the two "discussed with our partners how we can step up worldwide efforts to increase pressure on Pyongyang, and find a peaceful solution to the ongoing threat North Korea poses to global security".
"They were very fearless men, very courageous men and women and I just want to thank them on behalf of all Australians".
"We took the name "Liberal" because we were determined to be a progressive party, willing to make experiments, in no sense reactionary but believing in the individual, his right and his enterprise, and rejecting the socialist panacea", Turnbull said.More news: British hope into Wimbledon semi-finals
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"They ran towards the danger while others were fleeing it".
Two Australian women were among those slaughtered by knifemen who drove a van into pedestrians before going on a stab rampage.
"They didn't think of themselves but went to help those who they saw in need".
Australian prime minister Malcolm Turnbull has taken aim at critics in the right of the Liberal Party in a speech in London overnight.
The UK and Australia are expected to agree a free-trade deal once we are free of the EU's customs union.
The two leaders met police officers and paramedics who responded to the June 3 attack.
"Discussions on an ambitious and comprehensive bilateral trade deal with Australia remain a priority for the UK", Mrs May is expected to say.
Mr Shorten's gap with Mr Turnbull, who is due to hold talks in the United Kingdom with Prime Minister Theresa May this week after attending the Group of 20 summit in Germany, has narrowed to 8 percentage points.