Sir Lindsay described reports that traces of cocaine had been found in areas of the Palace of Westminster accessible only to people with parliamentary passes as “deeply concerning”.
In a statement, he said that he expected to see “full and effective enforcement of the law” on the parliamentary estate.
Separately, another senior MP suggested sniffer dogs may have to be brought in to check for banned substances.
A report in the Sunday Times said detection wipes had found traces of cocaine in 11 out of 12 locations tested amid claims of casual use of the class A drug by a group of MPs.
The paper said that Commons officials received reports last month that cannabis could be smelt in the open space between Portcullis House and 1 Parliament Street.
The report came as the Government was about to launch a new crackdown on drug use with its 10-year drugs strategy.
In a statement, Sir Lindsay said: “The accounts of drug misuse in Parliament given to the Sunday Times are deeply concerning – and I will be raising them as a priority with the Metropolitan Police this week.
“I expect to see full and effective enforcement of the law.
“While Parliament provides extensive support services for any staff or Members who may need help with drug misuse – and I would encourage anyone struggling with such issues to take up such help – for those who choose to flout the law and bring the institution into disrepute the sanctions are serious.”
Senior Conservative MP Sir Charles Walker who chairs the administration committee, suggested drugs sniffer dogs could be deployed.
“The House of Commons has a long history of using sniffer dogs to detect explosives,” he told the Sunday Times.
“It may be that we now need to broaden the range of sniffer dogs … to include those which can detect drugs.”