In photos published by the Daily Mail at the time, the pair were seen riding a scooter together and enjoying lunch al fresco.
"Ach, I'm not really willing to talk about that," James told The Guardian about the photographs and ensuing media circus. "There is a lot to say, but not now, I'm afraid."
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Karwai Tang/WireImage; Arnold Jerocki/Getty Lily James (L); Dominic West
David M. Benett/Getty Dominic West and Lily James in October 2018
More photos showed the duo — who were filming a BBC adaptation of Nancy Mitford's classic novel The Pursuit of Love at the time — at the airport in Rome together on Oct. 12.
The latter photos came about just one day before West and FitzGerald, 49, publicly addressed the reports about his excursion with James.
On Oct. 13, the spouses kissed and posed for photographs outside of their home in London with a sheet of paper that read, "Our marriage is strong and we're very much still together. Thank you. Catherine and Dominic."
Reps for West and James haven't commented to PEOPLE.
RELATED VIDEO: Dominic West Kisses Wife, Declares Their Marriage Is "Strong" After Being Seen with Lily James
James, meanwhile, appears to be getting serious with boyfriend Michael Shuman, as the two were spotted strolling hand in hand in Los Angeles late last month. They were on their way to meet Shuman's parents, E! News reported.
Earlier this year, the English actress was spotted with the Queens of the Stone Age rocker in Suffolk, England, where she was filming her forthcoming film, What's Love Got to Do With It?
Last summer, James sparked romance rumors with Chris Evans. The two were first seen together in early July, when they shared a taxi after leaving Mark's Club in London. Days later, they were seen enjoying ice cream at a park near Buckingham Palace.