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Sir Paul McCartney and his estranged wife Heather Mills even managed to upstage the late Diana, Princess of Wales, as they arrived for their divorce hearing at the High Court this morning.

Ms Mills, who is thought to be representing herself in a case widely expected to set a new record for divorce settlements, turned up in a black Mercedes which came to rest in a disabled parking space alongside the court complex.

The former model, who lost a leg in a road accident in 1993, was ushered from behind the tinted windows of the vehicle and headed for the nearby court, its windows covered to stop anyone seeing through the doors.

Sir Paul arrived a few minutes later, smiling and looking relaxed in a dark pin-striped suit with a black and white knitted scarf draped casually around his neck. Questioned about whether he would settle the case today, he replied simply: “Good morning”.

Ms Mills was wearing a sober black top and skirt below the knee over a peach pink blouse and ankle boots. Her long hair hung over her shoulders.

She said nothing to reporters and signs on the doors of Court 34 read “No Admittance - Strictly Private”.

The McCartney divorce is to be a private affair but that fact did not stop scores of photographers and journalists hovering around the entrances of the Royal Courts of Justice in the Strand, Central London. The McCartneys' arrival even drew some observers away from the other media circus at the High Court – the inquests into the deaths of Diana and Dodi Fayed.

Sir Paul and Miss Mills will be battling over money and access to their child after a marriage that lasted less than four years. They married in June 2002, four years after Sir Paul’s first wife, Linda, died of breast cancer.

Sir Paul has a personal fortune estimated at £825 million – putting him at risk of facing the biggest payout in British legal history.

But unless one of them takes issue with the settlement being hammered out behind closed doors in the Family Division of the High Court and goes to the Court of Appeal, the figures and details may never be known to the outside world.

Since Ms Mills appears to have decided to represent herself after falling out with her former law firm Mishcon de Reya, it is quite likely that she will cross-examine Sir Paul herself.

The former Beatle is thought to have offered Ms Mills a package worth about £55 million, including a £20 million lump sum up front, but negotiations for a settlement have reportedly foundered on her refusal to sign a confidentiality agreement as part of that deal.

Legal experts say that the settlement should exceed the record £48 million that the businessman John Charman was told by the courts to pay his former wife in May last year – even though the McCartney-Mills marriage lasted only four years and the bulk of Sir Paul's fortune was amassed long before the couple met.

They have a three-year-old daughter, Beatrice, whose future will also figure large in the negotiations.

Suzanne Kingston, a family law expert, said: “Current estimates suggest that Heather is likely to receive anything from £50 million to £100 million as her final settlement."

The hearing, in a cavernous oak-panelled courtroom where the ceiling soars more than 30ft, is expected to last all week.

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