The WSJ investigation found markets were moving ahead of the release of official ONS data in a way that is consistent with leaks.
Sam Bowman, executive director of the ASI, said such insider trading must be taken extremely seriously by the government and the ONS.
"If flaws in ONS procedures are enabling market-moving leaks to take place, allowing some individuals to profit off secret information, then something has gone badly wrong," Bowman said.
"The Cabinet Office should review ONS procedures and consider substantial reforms in light of this new evidence."
Bowman suggested following the lead of the US, where suspicious market movements are rarely seen. He said data is released less than 24 hours after completion, and statistical reports are physically delivered to the President.
"An alternative option would be to make the process entirely open, so that the public (and the markets) can see ONS data in real-time as it is generated, and markets can price in new information immediately and openly," Bowman added.
"The ONS is already working on this, but today's findings should be an urgent call to action for them to speed up the process."