The judge told them that despite their celebrity status this was a "fairly routine, big money case".
New laws aim to open family courts to public scrutiny, meaning they can only ask for specific details - for example, those relating to their children - to be withheld from the public arena.
Countess Spencer was granted a decree nisi in March 2007 on the grounds of her husband's "unreasonable behaviour".
The Earl - the brother of the late Princess Diana - called time on their marriage in June 2006 when the couple's daughter Lara was four months old and their son was aged two.
Following their separation the aristocrat started a relationship with attractive American TV presenter Colleen Sullivan - though this ended last summer. He is now seeing Bianca, Lady Eliot, a 32-year-old former model and the widow of late peer Jago, Lord Eliot with whom she had three children.
No decree absolute has yet been granted to the Spencers because of a sticking point over the former marital home, a Georgian house previously owned by Pink Floyd guitarist, Dave Gilmour.
One of the 44-year-old's four children from his first marriage to Victoria Lockwood, 18-year-old Kitty was in court to support her father.
There was widespread publication of his divorce from Victoria in 1997, with the world's media camped in South Africa, where they maintained a home. He eventually agreed out of court to pay his ex-wife $1.8 million and give her a $250,000 home in Cape Town.