The prime minister says he only learned of security concerns around the ex-US ambassador earlier this week.
The warning comes after a north-west London synagogue was hit by an arson attack overnight.
The Royal Family will be remembering the late monarch at events on Tuesday - on what would have been her birthday.
The Sussexes' four-day tour of Australia appears to have fallen flat with some.
Nearby Kensington Gardens was closed on Friday and specialist emergency services units were deployed to the site.