The "Lewis" actor, 38, and the 30-year-old model have struck up a romance after developing a friendship on TV's "Bear Grylls: Mission Survive" last year, reported Female First.
"It's very early days but both Laurence and Vogue consider themselves an item. They're enjoying spending time together and have had some great nights out. It's very recently turned into a romance because they get on so well," a source said.
The pair first started getting close in April, a month after Laurence separated from his wife Billie Piper, with whom he has two children, and they hit it off because they have both been through major break-ups and Williams was able to comfort Fox.