Wiki has the two place names as possibly having a similar root. Adding in other info, Croxteth said to be a contraction of "Stochestede" (or stockade, place for cattle) and Toxteth from Crocker's staithe, Crocker being a person, Viking or not according to taste (did they really have Vikings round there and is it a Viking name?) and staithe a landing place (as in ships, for the loading and unloading of).
mmm
One of my family names is Fairam, or Farlam, or ffarlam or Fairlamb (far north of England) , also according to taste. (I like ffarlam, myself). If you look this up in a dictionary of surnames, you used to get stuff about chimneys that didn't smoke (as in lang may your lums not reek). However, about 20 years ago I saw a sign pointing to Farlam, a village in Cumbria. I have a copy from a 12th century roll mentioning a Roger de Farlam. One of the sources of surnames is place names, so Bingo. I notice that this origin has now been adopted by on-line dictionaries. It's supposed to come from places where ferns grow, chrise!
I lost my internet connection for most of yesterday and until about 9 am this morning