The Labour MP appeared at the Heart Centre in Bennett Road, Headingley, this afternoon in a discussion ahead of European Parliament elections on May 23.
Speaking about the view that politicians should simply “get on” with Brexit, he gave a counter-argument using an example of his time working with Eurojust - the European Union's judicial cooperation agency - for five years.
He said: In Eurojust, we'd share our intelligence on terrorist gangs, those that exploit children and women, and traffic people. There's many more of those trafficked people than you'd care to think."
Sir Keir told how it is necessary for the various countries to uniformly agree on aspects such as setting a common time for officers to arrest a cross-border gangs or where to put such criminals on trial.
"That goes on 24/7, and I know that the lives of people in Yorkshire and Humberside, from the operations I've been personally involved in, have been protected by that," he said.
"I couldn't 'get on' with chucking all that out the window."
Sir Keir the former director of Public Prosecutions and the head of the Crown Prosecution Service, also said Leeds was a "brilliant example of why we should keep close economic ties with the EU".
Speaking to The Yorkshire Post after the event, he said: "I went to Leeds University, I keep in touch very closely with Leeds, I still work very closely with the university on various things and I am very proud of the fact that Leeds is a leading centre on things like financial services.
"And then you've got the media industry coming both to Manchester and to Leeds - these are fantastic things, and that's why this sort of idea that the impact [of a badly negotiated Brexit] might be more on London than Leeds or Manchester is wrong.
"Actually, Leeds is doing incredible things when it comes to those sectors just at the moment. And that's why it's so important that they're safeguarded.
"I think every person, every family, every community in Leeds and Yorkshire who's invested in trying to get that better future for Leeds is entitled to expect us to protect it for them so they can take it on.
"The last thing they need is any disruption that's actually going to make it harder for them to continue that success rather than easier. So Leeds is a brilliant example of why we need that close economic relationship with the EU and why boring old technical things like customs unions and single market really, really matter.
"They are boring and technical but they're also about lives, about communities, about places like Leeds and making sure that we can build on that success."