Nigella Lawson and Charles Saatchi granted decree nisi

Saatchi, 70, and Lawson, 53, now have to wait for a decree absolute, which is usually issued six weeks and a day later, ending their marriage.

Earlier this month Saatchi accepted a police caution for assault after pictures were published showing him holding Laswon by the throat as they had an argument on restaurant terrace.

He said in a statement he had "clearly been a disappointment" to his wife, adding the couple have become estranged and drifted apart over the last year.

He said: "I am sorry to announce that Nigella Lawson and I are getting divorced.

"I feel that I have clearly been a disappointment to Nigella during the last year or so, and I am disappointed that she was advised to make no public comment to explain that I abhor violence of any kind against women, and have never abused her physically in any way."

In an announcement which is reported to have broken the news of the divorce to his wife, he added: "This is heartbreaking for both of us as our love was very deep, but in the last year we have become estranged and drifted apart."

He dismissed the incident as "a playful tiff" but then accepted a police caution for assault, which he said was done to stop the incident hanging over them.

In the past, Lawson has described Saatchi as "the exploder" due to his temper.

In his statement, Saatchi insisted his actions were not violent, saying that while he had his hands around Lawson's neck, "there was no pressure applied to her".

He said the pictures gave a wholly different and incorrect implication.

He added: "I am sorry that we had a row. I am sorry she was upset. I am even more sorry that this is the end of our marriage."

Neither the couple nor their legal representatives attended the hearing.

In Court 9 of the High Court's building at First Avenue House, 13 reporters listened along with the district judge as an assistant read out Lawson and Saatchi's names together with those of 14 other divorcing couples.

The judge asked: "Does any party or person wish to show cause against decrees being made or in the question of costs?"

A decree nisi is a statement saying the court sees no reason why a divorce cannot be granted.

It is thought the divorce will be rubber-stamped some time in September.

Pictures were published last month showing Saatchi holding his wife by the throat as they had an argument on the terrace of a restaurant.

He dismissed the incident as nothing more than ''a playful tiff'' but then accepted a police caution for assault.

He said he had done so to stop the incident ''hanging over'' them.

Lawson, who has subsequently been pictured without her wedding ring, has described him as ''the exploder'' in the past due to his temper.

Saatchi later told the Mail on Sunday that the pictures gave a ''wholly different and incorrect implication".

But he also told the newspaper: "I feel that I have clearly been a disappointment to Nigella during the last year or so, and I am disappointed that she was advised to make no public comment to explain that I abhor violence of any kind against women, and have never abused her physically in any way.''

The couple confirmed they would not make any financial claims against the other, ruling out prolonged legal arguments.

That is one reason why the so-called "quickie divorce" is progressing swiftly.

Court paperwork shows that Nigella Lucy Lawson applied to divorce Charles Saatchi on the grounds of his continuing unreasonable behaviour.

The marriage was said to have irretrievably broken down and an "order for financial relief" has been agreed between the petitioner and respondent.

On the petition before court, Lawson had ticked "Yes" to the question: "Is the respondent's behaviour as set out in your petition continuing?"

Lawson also confirmed in the document that they were living apart.

The document was signed by the popular cook and broadcaster on July 9.