The neutralizing antibody response to influenza virus is dominated by antibodies that bind to the globular head of haemagglutinin, which undergoes a continuous antigenic drift, necessitating the re-formulation of influenza vaccines on an annual basis. Recently, several laboratories have described a new class of rare influenza-neutralizing antibodies that target a conserved site in the haemagglutinin stem. Most of these antibodies use the heavy-chain variable region VH1-69 gene, and structural data demonstrate that they bind to the haemagglutinin stem through conserved heavy-chain complementarity determining region (HCDR) residues. However, the VH1-69 antibodies are highly mutated and are produced by some but not all individuals, suggesting that several somatic mutations may be required for their development. To address this, here we characterize 197 anti-stem antibodies from a single donor, reconstruct the developmental pathways of several VH1-69 clones and identify two key elements that are required for the initial development of most VH1-69 antibodies: a polymorphic germline-encoded phenylalanine at position 54 and a conserved tyrosine at position 98 in HCDR3. Strikingly, in most cases a single proline to alanine mutation at position 52a in HCDR2 is sufficient to confer high affinity binding to the selecting H1 antigen, consistent with rapid affinity maturation. Surprisingly, additional favourable mutations continue to accumulate, increasing the breadth of reactivity and making both the initial mutations and phenylalanine at position 54 functionally redundant. These results define VH1-69 allele polymorphism, rearrangement of the VDJ gene segments and single somatic mutations as the three requirements for generating broadly neutralizing VH1-69 antibodies and reveal an unexpected redundancy in the affinity maturation process.