Another image shows Mr Kagalovsky, who shortens his surname to Kay, with his arm around Miss Woodward in a bar as she clutches a red rose.
He is a former student at the prestigious St Paul's School in Barnes, West London.
Miss Woodward, a budding surgeon, who has suspended her studies Oxford University, has posted a series of images of her and Mr Kagalovsky on social media.
In one photo, uploaded just before Christmas, the couple grin as they pose in front of an ice skating rink.
We have decided to remove the article that previously occupied this page.
However, this is not a response to the accusations of plagiarism or misogyny.
His father, Konstantin, is the former vice-president of the oil company Yukos and the former Russian representative to the International Monetary Fund (IMF) who claims to be the owner of Ukranian TV station TVi.
Mr Kagalovsky Senior owns properties in London, New York, Moscow and on the French Riviera.
She and her husband were investigated in the late 1990s as part of a money laundering probe looking into claims that billions of dollars were illegally desposited in the bank by Russian mafia bosses. The couple met in Washington DC in 1993 when Mr Kagalovsky was Russia's representative to the International Monetary Fund(IMF).
Like most Russian oligarchs, including his friends Abramovich and the late Vladimir Putin enemy Boris Berezovsky, he built his business empire off the back of the mass privatisation of state assets after the fall of the Soviet Union.