Seven people have died and at least 40 are being treated in hospitals across the capital after a van ploughed into pedestrians on the bridge, followed by a series of stabbings around Borough Market on Saturday night.
Scotland Yard said three attackers were shot dead by armed officers.
As the emergency unfolded, the Met issued a message urging members of the public in the affected areas to “run, hide and tell”.
The guidance was prepared by counter-terrorism police to set out the steps people should follow in the event of an attack.
After the bombing in Manchester, the official terror threat level was raised to the highest – critical – amid fears further attacks could be imminent.
It was the first time the assessment had reached the most serious rating for nearly a decade and a huge security response was activated, with military personnel drafted in to support police.
Last weekend the threat level was lowered to the second highest category of severe, meaning an attack was judged “highly likely”.
It was revealed following the Manchester blast that security services had foiled 18 plots in Britain since 2013, including five since the Westminster attack.
The threat being confronted by the UK’s counter-terrorism agencies is seen as unprecedented, with 500 active investigations involving 3,000 subjects of interest at any one time.