The 64-year-old Bridget Jones and Love Actually actor attended one of the music star’s London dates in June along with his wife and daughter.
Speaking to Zoe Ball on her BBC Radio 2 breakfast show, Grant said: “I loved it. Couldn’t have enjoyed it more.
“They were so nice to us. And she (his daughter) was bopping up and down.
“And, meanwhile, I was doing tequila shots with Taylor Swift’s very nice boyfriend, whose name has slipped my mind – Travis.”
“We went crazy”, he added.
Speaking about the shots, he said: “It’s revolting, isn’t it? As long as you’ve got a bit of lime and some salt…”
Grant also discussed his role in new horror film Heretic on the radio programme and admitted he is “not good” with the genre.
He said: “I remember having to leave a cinema in New York with my brother after 10 minutes. We just looked at each other and said ‘No, too frightening’ – in our 50s – and then went to another film in the same multiplex, sat there, 20 minutes in, ‘No, too frightening’.”
He added: “The close-ups in this film are terrifying – I look like my grandmother.
“I mean, that literally could be her, but that’s good. It’s good for this particular film.”
Grant revealed he had attended a Swift concert earlier in the year when he said in a post to X, formerly Twitter, that the Anti-Hero singer had “an incredible show, an amazing and v hospitable team and excellent if gigantic boyfriend”.
Other famous faces who attended the European leg of her tour included the Prince of Wales, Prime Minister Sir Keir Starmer, Tom Cruise and Sir Paul McCartney.
– Swift’s juggernaut Eras Tour continues with forthcoming dates in Canada, and is set to conclude on December 8 in Vancouver.