Thanks for all the comments & ideas so far.
I've been trying to work out whether St Matthews Home for Female Orphans and "the Orphan school" were two different places or whether perhaps the home/school became St Matthews Home for Female Orphans at a later date, but I'm still not sure either way. I certainly haven't found any references to St Matthews as early as 1845.
If it was fee paying then I really don't know who would have paid it as all records indicate the entire family were as poor as church mice. I tried to see if there was any connection to the military as Sarah Ann's father had been pensioned out in 1818, but I didn't find anything to suggest that was the case.
Her death was registered by 'Caroline Marsh present at the death' but I haven't had much luck tracing her forward either

Sarah Ann had a younger sister, Eliza (my GG Grandmother), who would have been 2 when her father died in 1840, and 6 when her mother died. I'm not sure where she was placed after her parents died but in 1851 she was recorded as sister/visitor at the home of two older sisters in Twyford, and 5 years later gave birth to my G Grandfather in the Melton Mowbray workhouse.
I have a long list of records to trawl through when I eventually manage to get to Leicester so its looking like that may be my only hope of finding out anything - it certainly is a puzzler though.