TV chef Nigella Lawson and millionaire art collector Charles Saatchi moved a step closer to ending their marriage yesterday.

In a hearing at London's High Court, District Judge Anne Aitken granted the couple a decree nisi – the first legal step to ending their 10-year marriage.

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. Neither the couple nor their legal representatives attended the hearing.

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 confirmed in September.

Pictures 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 said the pictures gave a "wholly different and incorrect implication". But he added: "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 "quickie divorce" is moving swiftly.

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