"passed to Historic England"
.. isn't quite how it happened.
Historic England and English Heritage used to be the same organisation - English Heritage ratained the name and became a charity[1] focussed on management of the various sites that they have in trust for the nation.
Historic England was the rest of what used to be English Heritage - all the statutary parts and the bits that do Government work (advice on Listing et. al.).
[1] Government budget cycles really don't work with conservation work - sometimes budget would be allocated to work that, for some reason or other, couldn't be done that budget cycle. In becoming a charity, EH is freed from that budget cycle and can manage the budgets in a manner more appropriate for conservation of the buildings that they manage. Historic England remains a government organisation, reporting to DCMS.