Irony of the house
Tom initially does not want to go and live with his Aunt and Uncle, as he is the only child and there is no garden. However, after he begins visiting the secret garden at night, he doesn't want to leave the house.
Irony of progress
This text presents a contrast between the pastoral Victorian country house, and the modern apartments and parking lot in place of the garden. As such, we see the "progress" does not necessarily have a positive effect.
Irony of Mrs. Bartholomew
Initially, Tom is wary of Mrs. Bartholomew, an irritable elderly lady living in his Aunt and Uncle's apartment building. However, at the end of the text he discovers that she is actually Hatty. As such, Pearce encourages us to remember that elderly people were once young too, and are still the same person.