The presenter paid tribute to the city following the events on Wednesday, which saw five people - including the attacker - killed.
“Before we start the show, the terror attacks yesterday happened just a mile away from here, where we film ‘The Nightly Show’,” Dermot told viewers.
“Tonight we’re dedicating our show to London, to the people who live here, visit here and work hard to keep us safe here.”
He continued: “People say London isn’t Britain, but to be honest I think it is. Being a Londoner has nothing to do with whether you’re born here, nothing to do with the colour of your skin or the faith you follow.
“It’s about acceptance, tolerance, stoicism and respect. It’s about millions of people being able to live side-by-side, day-by-day in an exciting, vibrant, infuriating, beautiful city.
“And, as awful as yesterday was, we know that we’ll endure. My - and it is just my humble opinion - is it will make us stronger. We’ll go on living, working, playing, moaning and queuing together.
“So from all of us here at ‘The Nightly Show’ tonight: Here’s to London, and here’s to home.”
The attack took place near the Houses of Parliament in Westminster, with police later confirming they were treating it as a terrorist incident.
The attacker killed PC Keith Palmer, Spanish teacher Aysha Frade, American tourist Kurt Cochran and last night another victim, named as 75-year-old Leslie Rhodes, died in hospital. 40 people were also injured, some “catastrophically”.
‘The Nightly Show’ airs weeknights at 10pm on ITV.