The Spider-Man star, 24, shared a photo of Parkes on Instagram Sunday during their outing on a golf course.
The English actress, who is best known for her roles in Doctor Who and The Spanish Princess, also posted a candid photo of Holland on the golf course.
Holland first posted about Parkes on July 27 when he shared a captionless Instagram photo of the London-based actress, who wore a mask during their scooter outing.