He is then said to have taken two Apple Macs, a TV, a watch, printer, and audio recorder.
The paper reported that Prosecutor Henry Fitch told Hammersmith Magistrates' Court that Miss Smirnova obtained "a court judgement against her ex-husband, requiring him to pay her money."
Murray then went to the Chelsea home with an accomplice and "took a number of items".
Smirnova is a descendant of Pierre Smirnoff, who started the Smirnoff vodka brand in Moscow in 1818, and her mother is gymnastics champion Elena Kolesnikova.
She starred in the TV reality show Meet the Russians, which was about rich expats living in the UK.
Smirnova, of Kensington, and Murray, of Warlingham, Surrey, were released on bail and will enter pleas to the fraud charges at Isleworth Crown Court next month.
