surgery (n.)

c. 1300, sirgirie, "the work of a surgeon; medical treatment of an operative nature, such as cutting-operations, setting of fractures, etc.," from Old French surgerie, surgeure, contraction of serurgerie, from Late Latin chirurgia "surgery," from Greek kheirourgia, from kheirourgos "working or done by hand," from kheir "hand" (from PIE root *ghes- "the hand") + ergon "work" (from PIE root *werg- "to do"). Compare surgeon.

According to OED, the British sense of "session at which a Member of Parliament (or other public servant) is available locally to be consulted by constituents" is by 1951, from an extended sense in medical practice of "regular session at which a doctor receives patients for consultation" in a room or den set aside for that purpose called a surgery (by 1846). The word has been extended in Britain to other free consultations for advice.