Hi again Sarah,
Unsurprisingly the book doesn't mention any records as it's about Glasgow in general.
And i've just noticed a later bit about the "Willow" name.
Methinks you'd need a rather old map to understand what the author is talking about.
The mentioned "Fleming's Plan" might be what's needed!

--
"...I cannot give anything satisfactory as to the derivation of
Willow Acre.
It can have no reference to the English
Willow, as the Scotch
Sauch would at once exclude this notion.
Fleming's Plan shows minutely the region around us.
What is now "
St. Andrew's Street," is there marked as the "
Weel Closs;"
and, in M'Ure's time (1736) it goes under the name of "
The Baker's Wynd,"
which, he says "reaches East from the Saltmarket Street to
the Burn, and is of length 39 Ells, and 5 Ells and 2 ft. wide."
A Bridge crossed the Burn (the
Molendinar, of course,) fronting St. Andrew's Church (not then Built),
where the Inhabitants got the Water to "Brew their Ale," and Wash and Bleach their Clothes in
the Common Ground.
According to Scotch Lexicographers,
Weel signifies "a small Whirlpool or Eddy,"-
and as, both at the "End" or Eastern extremity of the "
Weel Closs," and down at
"
Castle Boins," at the South-East of our
Weel or
Willow Acre,
- the same Ablutions went on, the
Eddy or
Weel may have been transformed into
Willow.
I admit, however, that this Interpretation may be more ingenious than orthodox..."
--
Jack