Mr. Putin may have realized how weak Mrs. May is, which is why he would decide to act now to take revenge on a man he sees as a traitor and to cause Britain new headaches.

Russia’s motivation is understandable. Its economy faces serious structural problems, including a dangerous overreliance on oil and gas. At the same time, business leaders are worried about the country’s long-term demographic decline. Mr. Putin seeks to bolster his domestic popularity by looking powerful as he sows discord with the West.

And Britain has made itself an easy target for Russian intrigue. To be fair, this is not a problem of Mrs. May’s making. The government is reaping the dubious rewards of having opened the City of London since the late 1990s to foreign capital with no questions asked about its origin. The initial aim of this permissive approach was to persuade investors that London — rather than New York — was best suited to be the world’s financial capital. Among the many to take advantage of the light-touch regulations were oligarchs, spies and gangsters.

Britain needs to make a concerted effort to ascertain where all of this fabulous wealth comes from. Russian oligarchs have made an indelible mark on London. Some own newspapers, others our most successful soccer clubs, while many more own huge chunks of high-end property in the most fashionable parts of the capital.

And some of those characters are close collaborators and friends of President Putin. British newspapers have been full of articles about Russian oligarchs and their relatives buying luxury London houses through anonymous companies. Reports say that this is now an ever more popular trick — squirreling away corrupt money by passing it on to relatives in the hope that it will evade scrutiny.

If Mrs. May is convinced that Russia is behind this attack, then she needs to devise a way of getting to President Putin’s friends and collaborators. And that means great transparency. She should reintroduce the stalled proposal to force anonymous companies to reveal the sources of their cash. If any members of Parliament or the cabinet tried to oppose a move now, their motives would immediately look suspicious. Now is the moment to confound her critics by acting decisively.

If Britain knows where the money is coming from, it can develop smarter sanctions against Mr. Putin’s inner circle. But that information has the added advantage of making it easier to spot criminal money from across the world being laundered through London’s real estate and financial industries.

If Moscow is indeed responsible for the poisoning of Mr. Skripal and his daughter, then the attempted murders look like another tactic in a strategy that seeks to exploit the political vulnerabilities of our democracies. But unlike fake news and the meddling in elections, this one could prove deadly.