Police bosses plan to move from Scotland Yard as they face making cuts of more than £500 million.
Deputy Commissioner Craig Mackey told the Mayor's Office for Policing and Crime that the force hopes to save around £6.5 million per year by moving to a smaller headquarters.
New Scotland Yard has been in its current location in Victoria Street since 1967 but Mr Mackey said it would take an investment of around £50 million to bring the building up to scratch.
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In a wide-ranging Peston on Sunday interview, he said Parliament security needs reviewing and the PM's counter-terror strategy is flawed.
The terror attack carried out by Khalid Masood at Westminster that left four people dead lasted less than two minutes say police.
Two knives were found at the scene in Islington, North London, and the suspects fled on foot before being arrested.