Possible Etymology of the Name Woolums
I discovered a reference in The History of the County of Gloucester by Thomas Rudge and Robert Atkyns on page 148 that the place name "Walham - Mead" was anciently "Wollams". I thenmade an inquiry to a British name studies program entitled EPNS asking for the etymology of the place name "Wollams" and received this reply: Walham (and the variants_Walam_,_Wallam(s)_) derives from the elements _walh_'a Welshman' and --_hamm_'a water-meadow'. The walh element is in the genitive plural, so the name is 'water-meadow of the Welshmen'.
The history referred to above recounts how a Welsh relegious order relocated to Goucester County many hundreds of years ago. Thus, the surname Wollams might have attached to a person who lived in this area north of the City of Gloucester.
You can read the refernce yourself at Google Books.