Our knowledge of this very early Dame School is limited. We are not even sure of the relationship between "Miss Wheeler's School" and "Mrs Wheeler's School".
The Reading Mercury on 20 October 1788 included:
"Hungerford. Miss Wheeler respectfully informs her friends that the Ball for her school will be at the Assembly Room of Wednesday November 12. Tickets 5 shillings to be had at the Bear Inn and at the School."
We are unsure just where "Miss Wheeler's School" was located, although a Sun Fire Insurance (for £100) of 1781 for what is now 15 High Street stated that George Jones was the owner of "one house and offices near the aforesaid (=16 HS), in the tenure of Wheeler." The Commoners List for 1781 also has "Widow Wheeler" for what is now 15 High Street.
George English kindly emailed (Sep 2016) saying "We have transcribed some family letters and Diary entries that may be of interest. These include: 14 July 1799 Margt Dobson came from Woodbro. Stayed till 24th when I took her & Elizth Barker to Mrs Wheeler’s school."
A Mary Wheeler's Boarding School is recorded in the 1796 Berkshire Directory, and an advertisement in the Reading Mercury for 13 Jan 1800 says that "Mrs Wheeler of Hungerford returns her grateful acknowledgment to her friends and the public, her school opens on Monday January 20th." - presumably the start of term, as Mary Wheeler died 13 Dec 1803, aged 60 years (see Headstone 179 in St Lawrence Churchyard). (Intriguingly, George English added "There's also a Diary entry "Mrs Wheeler died 25 Augt 1803" though this could be another Mrs Wheeler".)
The adverts in the Reading Mercury continue until 30 Dec 1805, when it's announced that "Miss Batten has taken over from her late aunt Mrs Wheeler".