  We analyse the structure of Yukawa couplings in local SU(5) F-theory models
with $E_7$ enhancement. These models are the minimal setting in which the whole
flavour structure for the MSSM charged fermions is encoded in a small region of
the entire compactification space. In this setup the $E_7$ symmetry is broken
down to SU(5) by means of a 7-brane T-brane background, and further to the MSSM
gauge group by means of a hypercharge flux that also implements doublet-triplet
splitting. At tree-level only one family of quarks and charged leptons is
massive, while the other two obtain hierarchically smaller masses when stringy
non-perturbative effects are taken into account. We find that there is a unique
$E_7$ model with such hierarchical flavour structure. The relative simplicity
of the model allows to perform the computation of Yukawa couplings for a region
of its parameter space wider than previous attempts, obtaining realistic
fermion masses and mixings for large parameter regions. Our results are also
valid for local models with $E_8$ enhancement, pointing towards a universal
structure to describe realistic fermion masses within this framework.
