In "The Destructors," the gang's motivation for destroying Old Misery's house is three-fold. First, the gang wants to raze the house to improve their prestige among the other street gangs. Blackie and the others feel that such a stunt would bring the Wormsley Common gang recognition and respect.
Second, the gang wants to destroy Old Misery's house because they distinctly do not trust Mr. Thomas. Even after his attempts to ingratiate himself by giving the boys some Smarties candy, the gang members still eye him with suspicion, commenting that he probably found the candy or stole it.
The final motivating factor for destroying the grand old house is to rebel against society. The boys collectively detest what the opulent old home formerly stood for, which of course is the superiority of the upper class. By tearing down the old house, the boys effectively declare their own independence and strength against the hierarchy of society.