Leaving the building yesterday Sir Paul gave his trademark two-fingered peace salute. But Ms Mills McCartney did not bother to acknowledge the press. Both declined to make any comment about the private hearing while their spokespeople said that it would be wrong to come to any conclusions on the basis of the parties' demeanour.
Sir Paul, sharply-suited, left shortly after noon accompanied by his solicitor Fiona Shackleton. They were followed three-quarters of an hour later by Ms Mills McCartney, who was wearing a beige woollen dress covered by a grey coat, black boots and her blonde hair tied back with a yellow hairband.
Later, the couple issued a short joint statement asking people to respect their privacy. It read: "Since the breakdown of the marriage there has been a significant amount of misreporting in the press. The parties both ask the media please to respect their privacy and the confidentiality of the proceedings, as they work to settle the outstanding issues between them in their divorce."
In the past, Ms Mills McCartney has adopted a more aggressive public relations strategy than her husband - talking openly about the breakdown of their marriage. Last year, the former model spoke out in a two-part television interview in America in which she said that she had been "madly in love" with Sir Paul and vowed never to marry again.
"I would rather someone come up and chop off all my limbs than go through what I went through," she said. "If your limbs are chopped off you ... get another limb and there's light at the end of the tunnel. When you're vilified for doing nothing but falling in love with an icon ... I'd rather have all of my limbs cut off, that's the God's honest truth."
But she insisted that she had kept quiet despite the "rubbish" that had been written about her since her marriage collapsed. "I just thought everybody would blame me," she said. "So I sort of had my head down and people would come up and go, 'How are you?' People want to come up and give me a hug."
She also dismissed suggestions that she married Sir Paul for his money. She said: "I was just madly in love, blinded by love. I'm a good mother, I'm a good person. I fell in love for the right reasons. I loved unconditionally, and it just didn't work out."