For Hong Kong, the deal faltered in part on political concerns. The London Stock Exchange cited the Hong Kong government’s sway over the Asian’s exchange’s parent company as a potential regulatory stumbling block. The territory’s government names a majority of the members of the Hong Kong exchange’s board. Hong Kong law also prevents anyone from acquiring more than 5 percent of the shares in the Hong Kong exchange without the local government’s approval.

More broadly, Hong Kong’s position as a Chinese city that exists outside the mainland’s laws has become increasingly tenuous. Hong Kong has been roiled by four months of increasingly violent protests over the city’s relationship with the mainland, prompted by Beijing’s heavier hand in its affairs. Britain returned Hong Kong to Chinese sovereignty in 1997, but under an arrangement known as one country, two systems, it operates under its own laws and runs its own justice system.

David Webb, a longtime shareholder activist who is a former board member of the Hong Kong exchange, said that it had always been unlikely that a deal would be completed. Various regulators oversee different subsidiaries of the London exchange, and some of these subsidiaries are systemically critical to finance in Britain, such as one that handles interest rate swaps, he said.

The proposed deal “was very unlikely to satisfy all of the different regulators,” Mr. Webb said. He added that British regulators were unlikely to have looked kindly on any bid from a company under a foreign government’s control, and even less likely if that foreign government were part of an authoritarian country like China.

At the same time, neither the Hong Kong government nor Beijing would be likely to agree to give up the Hong Kong government’s influence over the city’s stock market so as to make it easier for the exchange to do overseas deals, Mr. Webb added.