Some articles mention that Michael Middleton did have a trust fund of his own, some GBP200,000 or so. He and Carole supposedly used this to finance Party Pieces. I do think that Michael's family had/has money, but perhaps Michael and Carole could not finance their schools because, with a small trust fund, that is really not enough to pay for all those years at Marlborough. Most people, even those from wealthy families and with trust funds, do not really come into the true wealth of the family until the parents and grandparents die. I'm sure Michael inherited a pretty tidy sum when his parents passed away. (I know his mother has... Has his father, as well?)
Michael and Carole obviously wanted to make their own money to support their family how Carole wanted, before Michael inherited anything, because, obviously, that would be too late to send a child to boarding school.