London will not be stopped by terror, Metropolitan Police Commissioner Cressida Dick has said as she highlighted an increased visible police presence on the capital's streets.
Ms Dick spoke as she joined officers on some of the city's busiest streets, travelling on the Tube to Waterloo Station and patrolling the tourist hot spot of the South Bank.
"London has not stopped after other terrible attacks and it will not stop after this one," she said.
The Commissioner said the public should feel "utterly reassured" by the presence of police.
"I've been out and about today. The public seem to be very positive about the number of officers that we have," she said.
"The great thing about London is that we don't give in, we don't give in to terrorists - we never have and we carry on.
"So the transport system is running just as it ever did and the events are going ahead today.
"People are out and about. I've spoken to lots of people, Londoners and tourists and business people. People are here and I would say, carry on about your business and secondly, of course, be vigilant."
She added: "My main message is London is carrying on. Carry on with your business but be alert, don't be alarmed but make sure you tell us anything that worries you."
She described the bombing as "absolutely appalling, horrendous".
"I went to the scene last night, so I'm really proud of everybody who coordinated that response. But it must have just been utterly awful for everybody on that train and especially those who were badly injured.
"It's a very fast-moving investigation. We've got the full weight of the counter-terrorist police network.
"We've got our colleagues in the intelligence agencies and Government helping in every way they can.
"We are making some very considerable progress.
"You will have seen the announcement of an arrest earlier on in relation to this."
She said police would continue to work as hard as they could to reduce the threat to the country, and to discover who carried out the bombing and whether there was anybody else involved.