As pro-democracy protests in Hong Kong escalate, so does China’s fury. The unrest is now in its ninth week. It has evolved from limited, student-led opposition to a proposed extradition law into a broad-based, fully fledged challenge to Beijing’s rule. It is threatening to undermine China’s control of the former British colony and President Xi Jinping’s control of China. His quasi-dictatorial authority is on the line. A critical tipping point is in sight.

How long before China’s tough-guy leader, accustomed to getting his way and not averse to using force, loses patience?

How long before China’s tough-guy leader, a man accustomed to getting his way and not averse to using force, loses patience? How much longer can angry People’s Liberation Army generals be restrained? The Hong Kong garrison commander last week chillingly advertised his determination “to protect national sovereignty, security and stability”. And if a harsh military crackdown is ordered, and people begin to die in large numbers, what will Britain and the west do?

These questions are critical, because the struggle over Hong Kong’s future has far-reaching international ramifications – symbolic, political and practical. The crushing of its freedoms would be a grim triumph for the advancing forces of global authoritarianism. The economic impact on already volatile world markets and trade, where Hong Kong’s role is central, could be massively disruptive. And it would raise fundamental questions about the Xi ascendancy and China’s direction of travel.

If only for that last factor, it seems clear Xi will not resort to force, and de facto direct rule from Beijing, unless he feels he has no choice. He knows the outcome of such action would definitively give the lie to the favourite Communist party conceit of China’s “peaceful rise”. Xi knows the overseas repercussions could be immensely damaging, dwarfing in intensity the criticism of the abuses endured by Xinjiang’s Muslim Uighurs.

But it is also clear that the fury and frustration felt in Beijing is close to boiling point. There have been dozens of official warnings in recent weeks about the necessity of enforcing a harsh policy of “zero tolerance”, and of how the protests challenge “the bottom line of the ‘one country, two systems’ formula”. With Hong Kong at a defiant standstill on Monday, the angry rhetoric took on an even more threatening tone.

China’s outraged Hong Kong and Macao affairs office claimed, for example, that black-clad, masked protestors in Tsim Sha Tsui, in Kowloon, had flung the Chinese national flag into the harbour. “Their conduct has blatantly offended the state and national dignity … and greatly hurt the feelings of the entire Chinese people,” it said. “The central government will not sit idly by and let this situation continue,” the Xinhua news agency said.

The reappearance in public of Carrie Lam, Hong Kong’s chief executive, after an absence of two weeks, may be significant. Xi and other senior cadres in Beijing have hidden behind Lam since the unrest began, letting her take the flak, even though, in proposing the extradition law and generally chipping away at Hong Kong’s freedoms, she has faithfully followed the party line. Xi does not want Lam’s resignation, because that would be seen as a concession and sign of weakness – and could expose him personally to political fallout. Instead, Lam was sent out to face the media on Monday, lacking new ideas about how to defuse the crisis and peddling an uncompromising message.

“Such extensive disruptions in the name of certain demands or noncooperation have seriously undermined Hong Kong law and order and are pushing our city … to the verge of a very dangerous situation,” Lam said.

This was no random choice of words, rather a script approved in Beijing. Xi did not reach the top of the pile by tolerating “very dangerous situations”. When all is said and done, his is still the unrepentant party of Tiananmen Square, ruling from the barrel of a gun.

The potential for a violent Hong Kong security crackdown to trigger a truly international crisis is plainly growing. Jeremy Hunt’s embarrassing dressing-down by China’s ambassador, when he was foreign secretary, showed how little Britain could do in such circumstances – whatever the 1984 Sino-British joint declaration may stipulate. But as notional guarantor of Hong Kong’s freedoms and self-designated promoter of western democracy, Britain would surely be obliged to do something.

Here would be yet another crisis for which Boris Johnson’s government is unprepared, and unfitted, to deal with. Has anybody in Beijing ever heard of Dominic Raab, Hunt’s successor at the Foreign Office? What chance a favourable post-Brexit trade deal with China in such tainted circumstances? A crackdown would signal the final demise of the already tarnished Cameron-Osborne “golden era” in bilateral relations, and with it all hope of significant, sustained Chinese inward investment.

Quick Guide What are the Hong Kong protests about? Show Why are people protesting? The protests were triggered by a controversial bill that would have allowed extraditions to mainland China, where the Communist party controls the courts, but have since evolved into a broader pro-democracy movement. Public anger – fuelled by the aggressive tactics used by the police against demonstrators – has collided with years of frustration over worsening inequality and the cost of living in one of the world's most expensive, densely populated cities. The protest movement was given fresh impetus on 21 July when gangs of men attacked protesters and commuters at a mass transit station – while authorities seemingly did little to intervene. Underlying the movement is a push for full democracy in the city, whose leader is chosen by a committee dominated by a pro-Beijing establishment rather than by direct elections.

Protesters have vowed to keep their movement going until their core demands are met, such as the resignation of the city’s leader, Carrie Lam, an independent inquiry into police tactics, an amnesty for those arrested and a permanent withdrawal of the bill. Lam announced on 4 September that she was withdrawing the bill. Why were people so angry about the extradition bill? Beijing’s influence over Hong Kong has grown in recent years, as activists have been jailed and pro-democracy lawmakers disqualified from running or holding office. Independent booksellers have disappeared from the city, before reappearing in mainland China facing charges. Under the terms of the agreement by which the former British colony was returned to Chinese control in 1997, the semi-autonomous region was meant to maintain a “high degree of autonomy” through an independent judiciary, a free press and an open market economy, a framework known as “one country, two systems”. The extradition bill was seen as an attempt to undermine this and to give Beijing the ability to try pro-democracy activists under the judicial system of the mainland. How have the authorities responded? Beijing has issued increasingly shrill condemnations but has left it to the city's semi-autonomous government to deal with the situation. Meanwhile police have violently clashed directly with protesters, repeatedly firing teargas and rubber bullets. Beijing has ramped up its accusations that foreign countries are “fanning the fire” of unrest in the city. China’s top diplomat Yang Jiechi has ordered the US to “immediately stop interfering in Hong Kong affairs in any form”. Lily Kuo and Verna Yu in Hong Kong

Hong Kong could also prove a catalyst for a wider collision with Donald Trump’s United States. An unnerving confluence of events, including last week’s sudden threat of additional, punitive US tariffs and the ongoing row over American attempts to ostracise the Chinese telecoms giant Huawei has already sparked a significant sell-off and instability in global financial markets.

The Trump administration is increasingly at odds with China over its militarisation of the South China Sea, its ignoring of the US embargo on Iranian oil imports, its continuing support for North Korea’s nuclear-armed dictator, its so-called debt diplomacy in Africa and Latin America, and its “sinicisation” of religion, not solely in Xinjiang.

China in turn accuses the US and Britain of fomenting the Hong Kong unrest and plotting against it. Add to all this Xi’s belief that quasi-independent Taiwan, armed and succoured by Trump, has been emboldened in its “splittist” tendencies, and it’s not hard to see how the building anger in Beijing could yet trigger a bigger, more dangerous detonation.

• Simon Tisdall is a foreign affairs commentator