It says that the parties agreed to have it arbitrated, not that the father--who lost before the beit din--did not challenge the beit din's ruling before the british judge. There's not enough information here to know whether the british judge signed off on an agreed solution, or if he upheld the solution on the basis of an arbitration agreement. of course, if there is no arbitration agreement in the first place, then there is no basis in domestic law to accept the ruling of a beit din.
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from the article: British court accepts N.Y. rabbinical court’s divorce ruling