"Of course our thoughts are with those who have been affected by the terrible attack that took place in Berlin but Londoners should go about their business as usual. They should enjoy this Christmas period," she told 'Evening Standard' newspaper.
"It is important, I think, that we send a very clear message that we will not be cowed by the terrorists - that we will carry on with our lives as usual," she said, urging people to not be deterred from flocking to shops during the festive period by the attack on a Christmas market in Berlin.
In Trafalgar Square alone, throngs of 80,000 revellers have been recorded in past years.
"The security services and the police are working day in and day out to keep us safe... They are often unsung heroes but they are actually doing a very good job.
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"However, they have to be vigilant all the time and we should be very grateful for the work they do," May said.
Meanwhile, police in Germany have installed concrete barriers to prevent a repeat attack on Christmas markets across the country.
His ID and fingerprints have been found in the lorry, officials say.