Labour claims Prime Minister David Cameron has "serious questions to answer" about the government's approach to the plight of Christians facing persecution in Iraq.
Shadow foreign secretary Douglas Alexander said the UK's failure to follow France and Germany in offering them asylum will "no doubt raise grave concerns."
He added: "The UK government rightly took steps to help avert humanitarian catastrophe in Iraq and Labour has welcomed decisions to now offer support to the Kurdistan regional government and assist Kurdish forces with technical and logistical military equipment.
"But alongside steps to support the Kurdish forces, the UK must now work to engage regional partners to help build a more inclusive and stable government in Iraq.
"That regional approach must focus on supporting and stabilising Jordan, which now shares a border with the ISIS-held areas, as well as bringing countries like Turkey into efforts to secure regional stabilisation."
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The plans had been in development since 2014, but would help underline Britain as a "global player" following the Brexit result.
The number of calls about children suffering or witnessing emotional abuse or physical violence in the home has surged in recent years.
The curtain will come down on the show for the final time at the Piccadilly Theatre in March next year, before embarking on a UK tour.