London, Greater London - British art collector Charles Saatchi and his celebrity chef wife Nigella Lawson said on Monday they would not make any financial claims against each other to ensure a swift divorce.

Saatchi, 70, was cautioned by police last month for assaulting his 53-year-old wife, after pictures emerged showing him grabbing her neck at a London restaurant.

The pair, both multi-millionaires in their own right, said in a joint statement that the first stage of the divorce would go through on July 31.

"A divorce will proceed on the undefended basis, the decree nisi is to be pronounced on 31 July, and neither party will be making any financial claims against the other," they said.

They said Lawson had employed Fiona Shackleton, the divorce lawyer used by both Prince Charles and Paul McCartney, while Saatchi was representing himself.

"Both parties would appreciate privacy for themselves and their children at this difficult time," their statement said.

Saatchi announced his desire to end the ten-year marriage in the press earlier this month, just days after he was forced to defend himself against accusations of domestic violence.

The former advertising executive said the pictures of him with his hand around Lawson's neck showed a "playful tiff", but he accepted a police caution for assault.

The statement is Lawson's first public comment since the row broke out, causing her to leave the family home.

The daughter of former finance minister Nigel Lawson, she is a successful writer and TV presenter, dubbed "the domestic goddess" and famed for her flirtatious approach to cooking.

Saatchi, whom she married in 2003, made his money in advertising and now owns London's Saatchi Gallery of contemporary art.

Lawson has two children from her marriage to journalist John Diamond, who died of throat cancer in 2001, while Saatchi has one daughter from his previous marriage.

The normally publicity-shy collector said he wanted a divorce because Lawson had not come out publicly and defended him over the photographs.

"I feel that I have clearly been a disappointment to Nigella during the last year or so," he told the Mail on Sunday.

"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."