I found this tune in a collection of manuscript pieces written at the end of a 1746 edition of "The grounds and rules of musick explained" in Harvard’s Houghton Library, Theatre Collection.
Re: Red House
This is a Welsh version. In G major and a bit jollier!
T:Red House in Cardiff, The
BA|G2g2 gfe2|d4 c2B2|c2e2 edc2|BcBA B2G2|!
G2g2 gfe2|d4 c4|B2G2 FGAF|G2B2 G2:|
|:Bc|dcBA GABc|d2d2 dcBA|cBAG FGAB|c2c2 cBAG|!
dcBA GABc|d2d2 dcBA|BdBG AcAF|G2B2 G2:|