This piece suggests that it was an Accurist:
https://www.watchcrunch.com/Shakespe...ccurists-27395
"All four Beatles appear to have worn 9ct gold Accurist dress watches from the early 1960s. These were British manufactured mechanical watches with Swiss 21-jewel hand winding movements."
However, the author doesn't justify this claim. There are though some other photos of McCartney wearing what appears to be the same watch, and Lennon wearing a very similar piece from around the same time.
The same claim is made here: https://www.youtube.com/watch?v=jrHtalQHHBw
Accurist claim that The Beatles wore their watches here: https://www.accurist.com/about-us
"Accurist watches were catapulted into pop-culture, being seen on the wrists of British icons such as The Beatles and Twiggy"