Despite his wife having had an affair and the couple now living in separate houses, he says she is just "bored" and insists they still have a "few years" to enjoy life together. The only other way is to first live apart for five years.
Simon Beccle, Owens' attorney, said the public would find the decision "hard to understand".
Family law experts say the ruling shows there is a "divorce crisis" and called for the introduction of "no fault" splits. In their decision, they said that she had failed to establish that their marriage had irretrievably broken down.
This is despite pleas by Mrs Owens that the current state of the law is out of touch with changing social values.
The Supreme Court's decision today also means that getting divorced in England and Wales will remain, in principle, more complex than in dozens of other jurisdictions, including Chile, China and Russian Federation where "no fault" divorce exists (for more detail see Penningtons Manches' recent global barometer report).
Supreme Court President Lady Hale admitted she found the case "very troubling", while another said she had reached her conclusion without enthusiasm. But Mr Owens refuses to divorce her, denying his wife's allegations about his behaviour.
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A wealthy couple, the Owens had been married since 1978 and have two grown-up children.
The case "has sparked a debate about whether divorce laws in England and Wales need to change", says the BBC. The effect of this judgment is that Courts, lawyers and divorcing couples must ensure that a Petitioner's case contains adequate particulars of behaviour by which it can be said that the Petitioner cannot reasonably be expected to live with the Respondent.
Another said Parliament had "decreed" that being in a "wretchedly unhappy marriage" was not a ground for divorce. Whilst it is clear that the Supreme Court were not comfortable with that approach, they were ultimately hamstrung by the legislation and had to abide with it.
Lady Hale also confirmed that the behaviour complained of does not have to be the cause of the breakdown of the marriage and gave her strong concern that the trial judge may have underplayed the cumulative effect of a great many small incidents said to be indicative of authoritarian, demeaning and humiliating conduct over a period of time (at para 50).
As for Tini, it seems she will have to put up with Hugh for a little longer before a divorce is finally allowed to be granted in 2020. "Our role is only to interpret and apply the law that parliament has given us".
She took her petition to the court of appeal, where it was again dismissed. In 2016 there were more than 100,000 divorces in England and Wales.