Madonna and her former husband Guy Ritchie are still wrangling over arrangements for their children,The Times has learnt.

Earlier reports that everything was swiftly agreed are wide of the mark.

The pair had been thought to have agreed a compromise in which the two boys, Rocco, 8, and David, 3, who was adopted from Malawi, would divide their time between Britain and the US. Madonna’s daughter Lourdes, 12, would continue to live with her mother.

However, the pop star and her former husband cannot agree on where Rocco should go to school, with Mr Ritchie, 40, favouring England and Madonna the US.

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Peter Jackson, QC, a barrister specialising in children’s cases, is advising on arrangements for the children.

The couple hired two of Britain’s most highly sought-after family lawyers: Fiona Shackleton acted for the pop star, with Lady Ward, the wife of a Court of Appeal judge, acting for Mr Ritchie. They were divorced in a “quickie” hearing in November at the High Court.

The film director was reported to have taken no money, to avoid an unseemly public wrangle.

Subsequent reports indicated that, even if no lump sum were involved, the assets that he retained, including the couple’s country estate in Wiltshire, amounted to some £50 million.

Bernie Ecclestone, the Formula One racing chief, has decided to hire the same lawyer as Mr Ritchie for his own divorce proceedings.

Mr Ecclestone, 78, has left Withers, a top City law firm, and instead opted for Lady Ward at the London firm Manches. Mr Ecclestone, who is worth about £2.4 billion, has placed some £1.9 billion proceeds from the sale of 75 per cent of his Formula One business in an offshore account in his wife’s name. He therefore faces the problem of seeking to recoup hundreds of millions of pounds in any divorce settlement.

The racing chief had gone to Mark Harper, an expert in international divorce cases and offshore trusts. But The Times understands that he has been persuaded that he needs “the toughest divorce lawyer available”.

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