LONDON — For years, anticorruption campaigners have railed against Britain’s openness to ill-gotten riches from overseas and the foreigners who invest them. After a nerve agent attack on British soil, and the resulting diplomatic showdown between Russia and the West, that may be starting to change.

The British government said this week that it would review the cases of 700 Russians who were granted visas to live in Britain largely because they could invest millions of dollars in the country. And it signaled an openness to cutting off access to British financial markets for President Vladimir V. Putin’s government in Russia.

The government’s expressed determination to crack down on dirty money came on a day of rare good news in the poisoning attack. Yulia S. Skripal, who with her father, Sergei V. Skripal, was assaulted with a nerve agent, “is improving rapidly and is no longer in a critical condition,” Salisbury District Hospital said on Thursday.

Her father, a former Russian spy, remains hospitalized in critical condition.

Downing Street has promised before to punish Russia, particularly after the 2006 assassination of the Kremlin critic Aleksandr V. Litvinenko with a deadly radioactive isotope. But it dropped the matter once the headlines disappeared.