The Ministry of Anxiety is Mark Forrest.
Originally it was intended as a midnight organisation to which his eldest daughter could send letters containing all her worries and fears, and from which he would reply as an agent of some hidden, governmental agency. However, it has instead taken on a life of its own, to become the banner for, hopefully a series of self-published books, starting with The Haunted Mansion.
The Ministry of Anxiety is not, nor has it ever been a real governmental agency and any advertisements published within the classified sections of reputable broadsheets are to be ignored.
There is no Gap
The Haunted Mansion is just a children’s book.
And to repeat – the Ministry of Anxiety is Mark Forrest and Mark Forrest is a real person.