Lord Patten of Barnes said the Prime Minister must follow the lead of Canada and Australia while also pressing the United States to agree with Britain about the dangers of Chinese intervention in the city.
He also agreed with Hong Kong leader Carrie Lam that the area is "close to the abyss", with near-daily and increasingly violent confrontations between protesters and police occurring in recent weeks.
The Conservative peer added a commission of inquiry is needed to assess the reasons for the demonstrations and the way they have been policed.
Lord Patten told BBC Radio 4's Today programme: "What's clearly needed is a process of reconciliation.
"It's the only way I think you'll put a cap on this and get back to peace and stability in Hong Kong, but it does need the government to move."
On what Britain could do, Lord Patten added: "I very much hope that our own prime minister will be as outspoken as the prime ministers of Canada and Australia have been in defence of Hong Kong's freedoms."
Australia's Prime Minister Scott Morrison has rejected Chinese claims that the protesters are "terrorists" and called on ms Lam to listen to their concerns.
“My view is one to seek to de-escalate things," he said on Tuesday.
“To encourage the Chief Executive of Hong Kong to be listening carefully to what people are saying in Hong Kong, and to work towards a peaceful and calm resolution.”
Asked if he believed Mr Johnson is keeping silent, Lord Patten said: "I think he's made a ritualistic expression of concern but what he should say to (US national security adviser John Bolton), who is here, that he very much hopes the Americans will agree with us that it'd be a catastrophe if China was to intervene in Hong Kong."
Also on Tuesday, Foreign Secretary Dominic Raab condemned the violence between police and pro-democracy protesters amid a second day of chaotic scenes at Hong Kong's airport.
"Concerning to see what's happening in Hong Kong and the worrying pictures of clashes between police & protesters at the airport," Mr Raab tweeted.
Concerning to see what's happening in Hong Kong and the worrying pictures of clashes between police & protesters at the airport. As I said to Carrie Lam during my call last week, we condemn the violence & encourage constructive dialogue to find a peaceful way forward.— Dominic Raab (@DominicRaab)August 13, 2019
"As I said to Carrie Lam during my call last week, we condemn the violence & encourage constructive dialogue to find a peaceful way forward."
Hong Kong is a former British colony which was returned to China in 1997.
Protests have taken place in the territory over the summer, initially triggered by controversial extradition proposals that would have allowed some suspects to be sent to mainland China for trials.
Despite the government suspending the planned legislation, protesters have pressed on with broader calls for it to be scrapped entirely and with demands for democratic reforms.
The Sino-British Joint Declaration signed in 1984 paved the way for the handover and stated Hong Kong would enjoy a "high degree of autonomy, except in foreign and defence affairs" and be "vested with executive, legislative and independent judicial power".