LONDON — As she probes for Russia’s vulnerabilities during a week of deepening crisis, Prime Minister Theresa May does not have to look far. Within a few blocks of No. 10 Downing Street, she could find opulent homes owned by members of President Vladimir V. Putin’s inner circle.

A short walk from Mrs. May’s office is an apartment registered to a company owned by First Deputy Prime Minister Igor I. Shuvalov, with a value estimated at $16 million. Roman Abramovich, a former member of the Russian Parliament and a longtime Putin associate, lives opposite Kensington Palace, in a house whose value has been estimated at $163 million.

The rupture between Russia and the United Kingdom deepened on Thursday, eleven days after a former Russian spy was poisoned with a military-grade nerve agent in a sleepy town in southwest England.

In a rare joint statement, the United States, Germany and France condemned the attack, calling it the first offensive use of a nerve agent in Europe since World War II. And in Washington, the Trump administration announced new sanctions against 19 people and five organizations implicated in cyberattacks.