The deputy mayor of London is facing calls to resign after it was claimed he urged Scotland Yard to devote less time and resources to investigating allegations of phone hacking.

Giving evidence to the Leveson inquiry into press standards on Monday, the former Metropolitan Police commissioner Sir Paul Stephenson said Kit Malthouse had raised concerns about the amount of money spent on Operation Weeting.

"On several occasions after Operation Weeting had started and I had returned from sick leave, the Chair of the Metropolitan Police Authority, Kit Malthouse, expressed a view that we should not be devoting this level of resources to the phone hacking inquiry as a consequence of a largely political and media- driven 'level of hysteria'," Sir Paul said.

In his written evidence to the inquiry, Sir Paul said that he had told Malthouse the Met had "little choice" but to "invest significant resources" into the investigation.

"Additionally the nature of some of the revelations of media behaviour, particularly towards vulnerable members of the public, made a reopening of the investigation inevitable, from an operational viewpoint," he added.

Malthouse is deputy mayor of London with responsibility for the police and chairs the Metropolitan Police Authority.

Labour MP Chris Bryant, who has long pursued the phone hacking scandal, said Boris Johnson should sack Malthouse.

"Today's revelation at the Leveson inquiry by the former Met commissioner about the actions of Boris Johnson's deputy makes it clear that from the highest political level Johnson and Malthouse have intentionally sought to close down the phone-hacking investigation," he said.

"This amounts to a clear political intervention designed to intimidate the Met into dropping an investigation.

"Considering that the investigation has thus far uncovered bribery of police officers by The Sun, mass criminality at the News of the World and a deliberate attempt to pervert the course of justice by News International, both Boris Johnson and Kit Malthouse's interventions show that they are more interested in protecting their cronies than in pursuing justice.

He added: "In any other country this kind of political manipulation would be considered wholly unacceptable and corrupt. It is no longer possible for Londoners to have confidence in the Met with Kit Malthouse sitting at the top table. Kit Malthouse should either resign or Boris Johnson should be forced to sack him."

Sir Paul resigned as London's top police officer in July last year over his relationship with a former News of the World executive editor Neil Wallis.

But a spokesperson for Malthouse said it was his job to "question and probe" the resource allocation decisions of the Commissioner in order to secure an efficient and effective police force for London.

"It was entirely proper, as Paul Stephenson indicated this morning, for Kit Malthouse to probe the reasoning behind the allocation of resources into the phone hacking inquiry. Mr Malthouse has questioned the allocation of resources by the MPS in any number of areas, including knife crime, rape, murder and gangs. His job is to hold the Commissioner to account," they said.

"The Mayor has made it clear that the phone hacking investigation has to be pursued relentlessly and thoroughly."

Responding to the row on Monday evening Ken Livingstone said: "“Chris Bryant is right. Either Kit Malthouse should quit his position as the deputy mayor for policing, or Boris Johnson should sack him. The Mayor’s deputy abused his position to influence a police investigation into serious criminal allegations."