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I do not know but would assume that it was the college/school attached to St Alphage Parish Church. There still is a St Alphage [C of E] School from Pre to Junior age. They have a web site so may be able to provide a little of the history.
Just a thought but could it be that 'college' is here being used in a somewhat broad way to simply mean a school. If so then the teaching would have been along the lines of any village school of the time - reading writing and arithmetic.