The most significant thing that they have in common is that neither activity serves a purpose other than creating a name and image for the gang. They pinch rides because they can, not to actually get anywhere. They destroy the house because they can, not because of anything that Old Misery has done.
It is just as significant to notice the difference between the two activities. Pinching rides gives the gang a reputation without hurting anyone or anything. It makes them stand out and feel "important" within disrupting society or bringing any real damage. However destroying the house is a personal battle for "T." It has a clear purpose, to destroy, and very real and extreme consequences.
The two opportunistic acts of the Wormsley Common Gang are reflective of disrespect for the law as well as youthful post-war behavior that reflects their nihilism and loss of innocence.
In the war-torn landscape of post World War II Britain, there is in the youthful Wormsley Common Gang (common, in addition to here referring to the place they live—Wormsley Common—is a word often used in British English to mean pertaining to the lower class) a rejection of the past that is reflective of disillusionment with the upper class, a class connected to the once powerful empire of England. Thus there is the plan of Trevor, who even rejects his upper-class name to be called T., to destroy the house of Mr. Thomas, a house that is an architectural relic designed by Christoper Wren, the acclaimed designer of the famous St. Paul's Cathedral.
In order to assert his antipathy for the upper class, who have rejected his architect father by reducing him to employment as a mere clerk, T. plans a systematic but nonetheless creative destruction of the house from the inside. Moreover, by the fact that T. burns the seventy £ 100 notes, declaring "We aren't thieves," it is apparent that the intent is not merely vandalism but is instead the creative enterprise of a disillusioned and nihilistic youth who have lost their innocence, just as free-riding on the city's transportation exemplifies.