In 1870-72, John Marius Wilson's Imperial Gazetteer of England and Wales described Drainage Marsh like this:
DRAINAGE MARSH, an extra-parochial tract in Boston district, Lincoln; near Swineshead. Pop., 9.
The location is that of Blacktoft Farm: the 1888 Sanitary Districts Diagram for Lincolnshire shows that "Drainage Marsh" was inset into the western edge of the parish of Wigtoft, and our superimposition of the Wigtoft parish boundary onto OS maps shows this to broadly correspond with Blacktoft Farm.
A Vision of Britain through Time includes a large library of local statistics for administrative units. For the best overall sense of how the area containing Drainage Marsh has changed, please see our redistricted information for the modern district of Boston. More detailed statistical data are available under Units and statistics, which includes both administrative units covering Drainage Marsh and units named after it.
GB Historical GIS / University of Portsmouth, History of Drainage Marsh, in Boston and Lincolnshire | Map and description, A Vision of Britain through Time.
Date accessed: 23rd May 2013
Click here for more detailed advice on finding places within A Vision of Britain through Time, and maybe some references to other places called "Drainage Marsh".