Prince Harry and Meghan Markle pretended to be strangers when they met up in a supermarket early in their relationship

• On Dax Shepard's podcast, Prince Harry opened up about going "incognito."
• Prince Harry said he and Markle once met up at a supermarket and pretended to be strangers.
• He said since he's moved to California he feels "a little bit more free."

In a new interview with Dax Shepard, Prince Harry opened up about the lengths he and his now-wife, Meghan Markle, went to in the early days of their relationship to avoid attention and keep things private before going public as a couple.

The Duke of Sussex served as a guest on Thursday's episode of Shepard's "Armchair Expert" podcast, discussing the level of scrutiny and attention he's faced his entire life being born in the public eye as a royal.

He also recalled one experience when he and Markle tried to meet up in a supermarket to stay under the radar.

He said he and Markle once pretended to be strangers so they could meet up for a date

Harry recalled the couple's initial time spent in London before the public knew they were dating, when they could go largely unnoticed together.

"The beauty of it is that the first time that Meghan and I met up for her to come and stay with me, we met up in a supermarket in London - pretending that we didn't know each other - so, texting from the other side of the aisle," he recalled.

He said people were giving him "weird looks" and coming up to him while he was trying to find Markle.

He recalled, "I was there texting her saying, 'Is this the right one?' She goes, 'No, you want parchment paper.' I'm like, 'OK, [whispers] where's the parchment paper?'"

He said he's had to go through great lengths to be 'incognito,' but it's been easier since he moved to California

He explained that while he did get to do "mundane" things growing up like going to the grocery store with his mom, Princess Diana, "a handful of times," adding, "there was very rarely a day that went by without at least one paparazzi jumping out from behind a car or something."

He also joked about how he's tried to remain "incognito" when out and about in the world.

"It was nice - you have a baseball cap on, looking down at the floor. You don't know how many times we've done that when you're walking down the street trying to stay incognito it's like, 'Woah, signpost. Oop! Someone's dog - hi.'"

He continued, "It's amazing what you see - how much chewing gum you see, how many people's shoes you see. It's a mess."

He said he feels like he can focus a little less on being incognito now this his family stepped back from royal life in the UK and now lives in California.

"Living here now, I can actually lift my head. I feel different, my shoulders have dropped, so [have] hers," he added. "We can walk around feeling a little bit more free."

He said he even gets to take Archie for rides on the back of his bicycle, which he "never would have had the chance to do" if he and Markle stayed in the UK.

Prince Harry has often spoken about his desire to do 'ordinary' things and maintain a sense of normalcy

Prince Harry has often spoken about his interest in living a "relatively normal life."

Prior to his and Markle's engagement in 2017, he told Newsweek, "People would be amazed by the ordinary life [his brother, the Duke of Cambridge] William and I live. I do my own shopping."

"Sometimes, when I come away from the meat counter in my local supermarket, I worry someone will snap me with their phone," he continued. "But I am determined to have a relatively normal life, and if I am lucky enough to have children, they can have one too."

The royal also added, "Even if I was king, I would do my own shopping."