Green’s Dictionary of Slang

thatched house (under the hill) n.

also reed-roof’d-cot, thatch(ed) cottage
[thatch n. (2), but note Thatched House Lodge, Surrey, built for the keepers of Richmond Park in 1673 and subseq. owned by prime minister Sir Robert Walpole (1676–1745)]

the vagina.

[Scot]Order of the Beggar's Benison and Merryland (1892) 76: The small thatch’d house bneeath the hill, / Or fountain in Hair Court, sirs.
[UK]G. Stevens ‘The Trio’ in Songs Comic and Satyrical 13: When Love, grown bold, / Knock’d loud at Labour’s door. / Awhile within the reed-roof’d cot / They stood. [Ibid.] ‘The Sentiment Song’ 125: Here’s the Down Bed of Beauty which upraises Man, / And beneath the Thatch’d-House the miraculous Can. [Ibid.] ‘Administration’ 154: Ministers may Places fill, / I buy none, nor am selling; / A Thatch’d House underneath the Hill.
[UK]Harris’s List of Covent-Garden Ladies 72: The grove below is well thatched, and ample enough in size to take in any guest.
[UK]‘Bumper Allnight. Esquire’ Honest Fellow 44: I have a tenement to let, / [...] /Near a rising hill, sir / [...] / A drop of rain can ne’er get in, / It is so nicely thatch’d, sir.
[UK] ‘Rummy Toasts And Sentiments’ in Black Joke 45: The thatched cottage, at the bottom of Snow Hill.
[UK]‘Toast’ in Secret Songster 48: May the thatch’d cottage in Thy Lane always have a standing tenant.
[UK] ‘The Chapter of Smutty Toasts’ in Icky-Wickey Songster 8: Here’s the thatched house, the miraculous can!
[UK] ‘Toasts And Sentiments’ in Gentleman’s Spicey Songster 48: Here’s the thatch cottage of content.
[UK]Farmer & Henley Sl. and Its Analogues.