Epithelial organogenesis involves concerted movements and growth of distinct subcellular compartments. We show that apical membrane enlargement is critical for lumenal elongation of the Drosophila airways, and is independently controlled by the transcription factor Grainy head. Apical membrane overgrowth in grainy head mutants generates branches that are too long and tortuous without affecting epithelial integrity, whereas Grainy head overexpression limits lumenal growth. The chemoattractant Branchless/FGF induces tube outgrowth, and we find that it upregulates Grainy head activity post-translationally, thereby controlling apical membrane expansion to attain its key role in branching. We favour a two-step model for FGF in branching: first, induction of cell movement and apical membrane growth, and second, activation of Grainy head to limit lumen elongation, ensuring that branches reach and attain their characteristic lengths.