Although police will not release the name of the man involved, several U.K. media outlets have identified him as Lawson's husband, art dealer Charles Saatchi, CNN reported.
A representative for Lawson confirmed the chef and her children had moved out of their London home.
One tabloid's website carried the headline "Nigella Lawson attacked in public by Charles Saatchi" and published photos of Lawson and Saatchi at a restaurant with Saatchi's hand around Lawson's neck.
"Officers from the community safety unit at Westminster were aware of the Sunday People article which published on Sunday 16th June and carried out an investigation," a Metropolitan Police spokesman told CNN.
The spokesman said a 70-year-old man "accepted a caution for assault" at a police station Monday afternoon.
Saatchi told a London newspaper "there was no grip, it was a playful tiff."
Lawson, known as the "queen of food porn," has written numerous cookbooks and hosted television shows.