Katherine McPhee and Meghan Markle attended school together as teens

She may have been best known for her acting in legal drama Suits, but Meghan Markle has another lesser-appreciated talent.

She’s also a great singer, according to her former classmate Katharine McPhee.

McPhee previously shared a stage with Markle when they were both at Immaculate Heart High School in Los Angeles.

“She was actually in my sister’s class — two years older than me. My sister did shows with her, I did two shows with her when I was a seventh-grader or eighth-grader. They were obscure musicals. I think one was called Yankee Doodle,” McPhee, 34, tells PEOPLE exclusively. “I don’t know if there are videos of her singing, but she’s a really good singer.”

Meghan Markle and Katharine McPhee
| Credit: Katharine McPhee/Twitter

McPhee, who is settling into London where she’s reprising her role of Jenna in the hit show Waitress (she performed it on Broadway last summer), shared a picture of Markle and herself from their school days recently.

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And she hopes that the pregnant Duchess of Sussex might be able to fit in a date night and come and see the show with Prince Harry one day. “It would be a nice treat to give them an entertaining evening. But we’ve no expectations,” McPhee said between rehearsals and performances. “We would love for anyone to come and enjoy the show.”

Meghan Markle and Katharine McPhee
| Credit: Karwai Tang/WireImage; Mike Coppola/Getty

The star, who had been enjoying the spring sunshine in London while hunting for an apartment — “I’m loving exploring the neighborhoods” — says the early weeks of the show have underlined how the young British audience have taken to it. “People are going crazy for it here,” she says. “The audiences make it feel like a rock show, a rock concert … they’re going wild.”

But recently she has had to do that exploring sans fiancé David Foster, 69, who is based at home in Los Angeles.

"Waitress" At The Adelphi Theatre - Photocall
Katharine McPhee
| Credit: John Phillips/Getty

Her character Jenna becomes a mother in the show. Asked if motherhood is on the horizon soon, she says: “Do I have plans to become a mother? I’d like to be a mother at some point, [but] I’m focused on getting through the run of the show and then figuring out the next phase is.”

McPhee says that shows like hers, Wicked and Hamilton and Dear Evan Hansen, have brought musicals to a much younger audience. “More than half the fan base of Waitress are younger audience-goers than I am. There’s a really strong fan base,” she adds.

And in the U.K., it is even more so. “I feel it is even more so here. I feel the fandom here is even younger here. That demographic is very strong here.”

They are about three weeks into the run. “We are almost out of what I think is the hardest cycle, which is rehearsals during the day and shows at night and not having the full day to recover from the show.”

Her experience of the Sara Bareilles hit has been helpful. The prop department and stage hands department “have asked me a lot of questions,” such as whether the cooking utensils or flour are in the right place? “Yes. It’s the little details,” says McPhee.

“It’s such a prop-heavy show and they might ask me if this goes here or there. I think it’s been at least a little helpful that I have at least done it for a few months before I came here,” she explains.

And for any visiting American fans who may have seen the show on Broadway, it isn’t exactly the same. “There’s a little fairy dust dropped here and there, little tiny changes so people who have seen it before [might notice]. It’s such a great show and the cast is really remarkable.”