LONDON — The United States on Tuesday ratcheted up its efforts to block Kremlin-linked industrialists from doing business in the West, warning that British banks will have to sever their relationships with the tycoons if they want continued access to American financial institutions.

Sigal P. Mandelker, a top American Treasury official in London to meet with her counterparts, said British banks could face “consequences” if they continued to carry out significant transactions on behalf of the 24 influential Russians sanctioned by Washington on Friday. The list includes the industrialists Oleg Deripaska and Viktor Vekselberg, along with Kirill Shamalov, who American officials have identified as President Vladimir V. Putin’s son-in-law.

“These are blocking sanctions,” Ms. Mandelker, under secretary of the Treasury for terrorism and financial intelligence, said at a briefing with reporters. “There of course would be consequences for U.K. financial institutions” that continued to do business with the Russians.

The warning has resonated in London, which for decades has served as a haven for Russia’s wealthiest families. Russian investors own iconic British assets like the Chelsea Football Club and swaths of high-end London real estate, and they support thriving networks of lawyers, financial advisers and estate agents.