Alwyn, 27, walked the red carpet alone but linked up with the 29-year-old singer at an afterparty, witnesses on social media said.
Swift later posted a photo posing in a pale blue Stella McCartney gown, writing, "AHHHHH @thefavouritemovie just won seven @bafta awards !!!" she wrote. "Bout to go give some high fives - thanks @stellamccartney for this dressss."
Alwyn starred alongside Olivia Colman, Rachel Weisz and Swift's pal Emma Stone in "The Favourite," which was the BAFTAs biggest winner, taking home a total of seven awards, including the prestigious Best Film.
Swift lost out to the Best Pop Vocal Album Grammy to Ariana Grande.
The "Reputation" star's fans threatened to boycott the Grammys following Swift's loss.
Swift has been spending quite a bit of time in London as she films the movie adaptation of Broadway's "Cats."
She's been dating British actor Alwyn since October 2016, but the pair have taken pains to keep their relationship as private as possible.
Sources previously gushed that Swift thinks Alwyn is "The One," while the "Billy Lynn's Long Halftime Walk" star admonished press for asking about his superstar paramour, telling British Vogue, "I'm aware people want to know about that side of things. I think we have been successfully very private and that has now sunk in for people… but I really prefer to talk about work."