  A strongly reflective modular form with respect to an orthogonal group of
signature (2,n) determines a Lorentzian Kac--Moody algebra. We find a new
geometric application of such modular forms: we prove that if the weight is
larger than n then the corresponding modular variety is uniruled. We also
construct new reflective modular forms and thus provide new examples of
uniruled moduli spaces of lattice polarised K3 surfaces. Finally we prove that
the moduli space of Kummer surfaces associated to (1,21)-polarised abelian
surfaces is uniruled.
