The Merchant Taylors School is an exceedingly old one; it was set up originally to teach boys of the City of London, and many of its students have gone on to distinction, and even fame. I believe Edmund Spencer went there, just to give an example.
I really don't know much about it in JA's time, I'm afraid, but I get the distinct impression that its clientele was still the merchant classes of the City of London, rather than the Country squires and the Aristocracy. This perhaps puts the Thorpes on a par with the Steeles and the Gardiners. There's something else nagging in my mind...there is a connection with JA's family, I'm sure. I'll see if I can find it.
This is one of the annoying little details in JA's work that might be a major comment upon class and society, or may simply be a family joke.