The couple, who married nine years ago following the death of Lawson's first husband, the journalist John Diamond, are understood to have been at the end of their meal at Scott's, a popular venue for celebrities such as Pippa Middleton and Kate Winslet, when the argument broke out.
The pair are regular visitors to the restaurant, always choosing the same outside area screened by olive trees so Saatchi, dressed in his habitual dark suit and white open-necked shirt, can smoke.
One witness of the argument between the couple told the Sunday People: "It was utterly shocking to watch... It was horrific really. She was very tearful and was constantly dabbing her eyes. Nigella was very, very upset."
The paper reported that Lawson, 53, who has recently made the transition from British television screens to stardom in America, appeared to try to pacify her husband, placing a hand on his wrist and at one point leaning over to kiss him on the cheek.
Comments on social media expressed shock at the photographs as well as the failure of anyone to step in during the row.
Labour MP Luciana Berger tweeted: "A man reportedly grasps a woman's neck 4 times in public & no one intervenes, incl. photographer who took photos."
The television cook, who is the daughter of former Chancellor of the Exchequer Nigel Lawson, has previously spoken of a tempestuous side to her relationship with Saatchi but there has been no sign that the marriage is in trouble.
On the morning of their meal, Lawson tweeted a picture of her breakfast of smoked salmon and scrambled eggs and has subsequently sent further tweets about food. Her most recent post was sent on Saturday lunchtime with a picture of a cup of green tea and a toasted bagel.
In an interview in 2007 Lawson, spoke of the couple's contrasting temperaments, describing Saatchi as an "exploder" and herself as a "festerer". She said: "I'll go quiet when he explodes, and then I am a nest of horrible festeringness."
Despite his wife's status as the nation's post-modern Delia, Saatchi has said her cooking is "wasted" on him. Lawson once commented: "Charles doesn't really like proper food. He prefers a bowl of cereal."
- INDEPENDENT