I will add what others have posted before, that 'Cheap' is from an old root word, Middle English chep, from Old English cēap (m-w.com), meaning 'trade.' It really meant that the streets named that ran through a marketing section of town.

Shapard says the lower, older part of the city was near where originally stood the West Gate into Bath. (vol. ii, ch. v, note 11) It is not surprising that more than one landmark took that name, just as a street today named, oh, Founders' Bridge Road might be close to a Founders' Bridge St., and a Founders' Bridge Avenue. Morrison does say it is blocks away from any fashionable address, and in close proximity to some rather shady parts of town. (vol. ii, ch. 5, note 2)