Asylum claims would be dealt with by the Home Office, not the High Court.

Any divorce/financial proceedings arising out of divorce take months to get off the ground and get a Court listing and there are jurisdictional issues to overcome.

That only really leaves extradition proceedings and child abduction proceedings.

The UAE is not a signatory to the Hague Convention on child abduction so the English Court isn't obligated to return the children, in the way they would be if they were abducted from signatory countries such as France or Canada.