If there's a chorus which goes "Titty-fa-la-tiity-fa-lay" then Bill is right it's a Geordie song called "Little Chance". There are two versions of the song with the same tune and chorus. The original was all about a pit-pony called "little Chance", but a Geordie Music Hall singer added the comedy verses including the "Hands upon her calves" one.

The folk process continues, however, because my mate Dave Blagrove has modified it to a Canal Song called THE SINGLE BOLINDER which also uses the Music Hall verses