This is the most limited collection but growing. I am finding entries from a range of sources - checking forwards from 1861 and backwards from 1881, mainly. This way you do find some additional entries. There are now almost 500 entries here. Please contact me if you know of any teachers in the 1870s and I can add them.
Of the people listed as educators in 1871 that I have found so far, there were a number at the West Derby Union Workhouse. Some of these were working there - of whom two pupil teachers, aged 13 and 15, may be previous inmates; others were established teachers. There were four teacher inmates - three of them very elderly, and one who had a small child and is listed as epileptic.
There are also a range of exotic birthplaces, including Samoa and Switzerland. Quite a few American born teachers too.
Download the list from here. There is a sheet of entries from the 1873 Directory but not yet located in the census. I’m working through it slowly! Any I definitely can’t find are listed in yellow - to be sought using wildcards etc. etc. later on.