The Gatehouse can be seen in the north east corner of this 18th century map: http://www.motco.com/Map/81002/SeriesSearchPlat...
The overlays that highlight 17th century London features are approximate and derived from:
Open location in Google Maps: 51.499121, -0.129158
Paul Brewster • Link
Wheatley does add the note that the Gatehouse was a prison.
vincent • Link
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
Thomas Edwards, a Reading chandler, was in the Gatehouse prison, Westminster for the same reason.
list of famouse residents including Hartlibb the sonne
Gate House, a prison near the west end of Westminster Abbey, by the way leading into Dean's Yard, Tothill Street, and the Almonry.
[SPOILER ALERT] In June 1690 Samuel Pepys was committed to the Gate House on a charge of being in communication with the exiled James II.; but in consideration of his ill-health, he was admitted to bail, and does not appear to have been troubled again.
---London, Past and Present. H.B. Wheatley, 1891.
Chart showing the number of references in each month of the diary’s entries.