Home Secretary Theresa May, who faced intense scrutiny during her efforts to deport Abu Hamza, said she was pleased that that the cleric "has finally faced justice" after using "every opportunity, over many years, to frustrate and delay the extradition process".
"His conviction was facilitated by this government's tireless work to successfully remove him from the UK to face trial in October 2012," she added.
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The plans had been in development since 2014, but would help underline Britain as a "global player" in the wake of 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.