A source recently told PEOPLE that Wilde and the musician "seem very serious" and "spend all their time together"
Olivia Wilde, Harry Styles
Olivia Wilde; Harry Styles
| Credit: John Shearer/Getty; Dia Dipasupil/FilmMagic

 Olivia Wilde and Harry Styles are heading across the pond.

The pair, who were first seen holding hands at a friend's wedding early last month, have been staying together at Styles' Los Angeles home "for a while" and left for England together after wrapping Don't Worry Darling, a source tells PEOPLE.

Wilde reunited with her kids, son Otis, 6, and daughter Daisy, 4, who have been with their dad Jason Sudeikis. The actor is currently filming the second season of Ted Lasso in London.

Wilde, 36, and Styles, 27, had been working together on the upcoming film, Don't Worry Darling, in L.A. The film is Wilde's highly-anticipated sophomore directorial project which she also stars in.

Earlier this week, Wilde praised Styles on Instagram for his work on the project as they wrapped filming the movie.

In the caption, Wilde explained how most male actors don't want to appear in female-led films and take the lesser role, which in turn makes those movies hard to finance. But Styles jumped in without reservation to play backup to Florence Pugh's leading role.

"Not only did he relish the opportunity to allow for the brilliant @florencepugh to hold center stage as our 'Alice', but he infused every scene with a nuanced sense of humanity. He didn't have to join our circus, but he jumped on board with humility and grace, and blew us away every day with his talent, warmth, and ability to drive backwards."

The heartfelt message comes weeks after Wilde and Styles were seen holding hands at a wedding in Montecito, California. A source confirmed to PEOPLE at the time that they had "dated for a few weeks," at that point.

Earlier this month, a source told PEOPLE the two "seem very serious" and "spend all their time together" while they shot the upcoming film.

"She is also very happy with Harry," added the source.

Sources also previously told PEOPLE that as Wilde and Styles spent time together on-and off-set, their friendship "quickly turned romantic," said an insider, who added: "Their chemistry was very obvious."

"Everyone saw it coming. During breaks, he hasn't been able to stay away and visited her trailer," the insider added.