The stepson of Malaysian Prime Minister Najib Razak bought a £23.25 million ($33.6 million) house in central London in 2012 with money originating from the troubled Malaysian state investment fund 1Malaysia Development Bhd., according to people familiar with the situation.

The redbrick four-story house, built around 1900, is part of a row set back from the road and protected by security gates, a short walk from Malaysia’s diplomatic mission in London’s exclusive Belgravia neighborhood. The registered owner of the house is Qentas Holdings Ltd., a company based in the British Virgin Islands. Mr. Najib’s stepson is the beneficial owner, the people said.

Investigators believe that money from the Malaysian fund known as 1MDB was used to buy the house in July 2012. The Wall Street Journal has previously reported that Riza Aziz, a film producer and stepson of the Malaysian leader, used money that originated from 1MDB to buy $50 million worth of properties in New York and Los Angeles and to finance the 2013 movie “The Wolf of Wall Street.”

A spokesman said last week that Mr. Aziz’s film company, Red Granite Pictures, “is responding to all inquiries and cooperating fully.”

“There has never been anything inappropriate about any of Red Granite Pictures or Riza Aziz’s business activities,” the spokesman said. “What they have done and will continue to do is develop and produce successful and acclaimed movies that have generated more than $825 million in world-wide box-office revenues.”