Daily entries from the 17th century London diary
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The Gatehouse can be seen in the north east corner of this 18th century map: http://www.motco.com/Map/81002/SeriesSearchPlatesFulla.asp?mode=query&title=Tothill+Street&artist=384&other=384&x=11&y=11
Wheatley does add the note that the Gatehouse was a prison.
it had some very famouse residents:
Transferred to the gatehouse at Westminster, he was so abominably treated that his father petitioned Elizabeth that he might either be brought to trial and put to death, if found guilty, or removed in any case from that filthy hole. Southwell was then lodged in the Tower, but he was not brought to trial until February 1595
http://30.1911encyclopedia.org/S/SO/SOUTHWELL_ROBERT.htm
Thomas Edwards, a Reading chandler, was in the Gatehouse prison, Westminster for the same reason.
http://www.users.globalnet.co.uk/~hadland/tvp/tvp9.htm
list of famouse residents including Hartlibb the sonne
http://www.tower-of-london.com/prisoners/book.html