In a hearing at London's High Court which lasted less than a minute, District Judge Anne Aitken granted Nigella Lawson and Charles Saatchi a decree nisi - the first legal step to ending their 10-year marriage.
Saatchi, 70, and Lawson, 53, now have to wait for a decree absolute, which is usually issued six weeks and a day later, ending their marriage.
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The Labour leader did not say whether he would maintain Britain's nuclear deterrent programme.
Ukip leader Paul Nuttall also said he would want to get rid of Sharia courts.
Over 40,000 people picked up their packs to take part in the annual marathon in the capital.