Bred by Mr Smith of Middleham, Yorkshire, and later owned by Richard Williams of Cheshire, Squirrel was a full-brother to Easby Snake, the sire of Mother Western, she the 2nd dam of Eclipse (ch c 1764 Marske). Racing from 1724 through 1726, generally in four-mile heats, he was said to be the best horse of his time for high weights.

Following his career on the turf Squirrel was sold to Ambrose Cowley for 500 guineas. After Cowley's death Squirrel returned to Richard Williams who owned him until his death. In the stud his sole contribution¹ appears to be Fair Helen, the taproot mare of Family 10.

The pedigree given below for Squirrel differs from that recorded in the General Stud Book in that his second dam is shown as a daughter of the Layton Grey Barb instead of as a daughter of a Son of Pulleine's Arabian, also called Rockwood. Highflyer presents evidence that this son was also sometimes known as the Layton Grey Barb.

The General Stud Book [1:413] also states that Williams’s Squirrel was sometimes referred to as Lister’s Squirrel. This statement is difficult to accept for three reasons. First and foremost, there is no trace of any Mr Lister among the known owners of Williams’ Squirrel.

Second, "Lister’s Squirrel" was, according to both Pick and Cheny², another name for Fox Cub, whose pedigree is entirely unrelated to that of Williams’s Squirrel. The identification of Lister's Squirrel with Fox Cub makes more sense because Fox Cub and his close relative, Fox, were both bred by Sir Ralph Assheton and the husband of Assheton's daughter Catherine was Thomas Lister. Thomas and his wife appear to have acquired Fox and Fox Cub following the death of Sir Ralph, which occurred in 1716, when both colts were two years old. (Fox Cub’s race record clearly shows that he ran for "Mr" Lister – probably Thomas, not Matthew³ – under the name of Squirrel; it is not clear when he began to be called Fox Cub).

Third, one of the mares specifically said in the General Stud Book to have produced a daughter by Lister’s Squirrel also has a daughter attributed to Fox Cub. This implies two possibilities: either the mare was mated to the same stallion twice, or there was in fact only one daughter, her sire having been known by two different names.

The sire of Williams’s Squirrel was Snake, also called Old Snake or Lister's Snake. Snake is presumed to have been the property of Matthew Lister, who stood his sire, known as Lister's Turk. It seems plausible enough to suspect that Williams’s Squirrel, son of Matthew Lister's Snake, was misidentified as Thomas Lister’s Squirrel simply because both had a connection to a Mr Lister. The confusion between two different horses could easily have been due to a failure to distinguish between two different men.

¹ The General Stud Book attributes two other offspring to "Squirrel (Lister's or Williams's)" [GSB1:413]: a filly from Family 8 who was the grandam of Sir R Grosvenor's Tweedle by Rib [GSB1:3], and another filly from Family 8 who was the dam of a filly by Hutton's Blacklegs [GSB1:7]. However, on page 3 there are two offspring recorded by Lister's Squirrel; the second one is also from Family 8 but has no known offspring. Additionally GSB records a Lister's Squirrel Mare from Family 56 who is thought to be the 4th dam of the American horse Batte & Macklin's Fearnought (b c 1777 Fearnought*) [GSB1:59; E1:233].