A former children's television presenter with the BBC has won a family court fight with an ex-partner over their child.

Katy Ashworth had brought the child back to Britain after a trip to Australia earlier this year.

Her ex-partner, Ben Alcott - who lives in Australia - had argued that the child was habitually resident in Australia.

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He had complained that Ashworth had been wrong to take the child back to the UK.

Deputy High Court Judge Alex Verdan, who analysed evidence over two days at a private hearing in the Family Division of the High Court in London, has disagreed.

The judge has concluded that the child was not wrongfully removed from Australia by Ashworth.

Judge Verdan had allowed reporters to attend the hearing - and report an outline of the case - but had barred the publication of the names of the people involved.

The judge has now produced a written judgment on the case and ruled that Ashworth and Mr Alcott can be identified.

He says the child must not be named in media reports.

Ashworth is best known for working on CBeebies.

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Her katyashworth.com website describes her as a "very well-known and much-loved face to thousands of children and their families across the UK and throughout the rest of the world" and says she is an "accomplished actress, entertainer and singer".

Judge Verdan had considered evidence at a hearing earlier this month.

Both Ashworth and Mr Alcott had been at the hearing.

He said, in his ruling - which was made available on Friday, that Mr Alcott was a 42-year-old television director and had lived in Redfern, New South Wales.

Ashworth was 30, British, and had lived in England for almost all her life.

"Until earlier this year the mother worked as a television presenter with the BBC," said Judge Verdan in his ruling.

"The parties started their relationship in May or June of 2011. They never married."

He added: "The parties' relationship was long distance given where they each lived. In addition, they separated and reconciled on a number of occasions."

Judge Verdan said Ashworth had always been the child's primary carer.

She travelled to Australia with the child in April.

"The father says this was a permanent move," said the judge.

"The mother says it was a trial attempt to see if their relationship would work out long term."

He said Ashworth and the child stayed Mr Alcott's home for three nights - and returned to the UK shortly afterwards.

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The judge added: "The main reason the mother left Australia was that she discovered material on the father's computer which indicated to her his infidelity."

He said Ashworth had emailed Mr Alcott, saying: "Ben. I know everything. I'm done. Have packed up and left."

She emailed again, after arriving back in the UK, adding: "Thank goodness I found out all the lies before moving to Australia with you for good."

Judge Verdan said Ashworth had discovered evidence suggesting that Mr Alcott was having relationships with four other women.

He said she had found "women's clothing" and "more importantly" messages on his Mr Alcott's computer from other women.

Mr Alcott had accepted that "on any reckoning" his personal life was "very complicated" and said it was "very difficult to balance the different female interests in his life" as his "decks were very crowded".

Judge Verdan said Mr Alcott wanted the child to be returned to Australia.

"His case is that the move to Australia was intended to be a permanent move and that immediately before the mother (and child) returned to England, (the child) was habitually resident in Australia," said the judge.

"The mother opposes the father's application asserting that (the child) never became habitually resident in Australia."

Judge Verdan ruled in Ashworth's favour.

"I found the mother's evidence to be clear and consistent and supported by the documents," said the judge. "I found the father's evidence to be inconsistent, unreliable and unconvincing."

The judge added: "My conclusion is that any agreement by the mother to move to Australia was based on a fundamentally flawed premise."

He went on: "If the mother had known the true state of affairs I am satisfied that in all likelihood she would not have moved to Australia with (the child) even for a trial period."

Judge Verdan concluded that the child had never "acquired habitual residence in Australia".

"I concluded that (the child) was not integrated to a sufficient degree in a social and family environment in Australia and that the mother was probably not integrated at all," said the judge.

"(The child) had not put down roots."

He added: "The mother did not wrongfully remove (the child) from Australia ... she did not abduct him."