  We study the effect of disorder on the London penetration depth in iron-based
superconductors. The theory is based on a two-band model with
quasi-two-dimensional Fermi surfaces, which allows for the coexistence region
in the phase diagram between magnetic and superconducting states in the
presence of intraband and interband scattering. Within the quasiclassical
approximation we derive and solve Eilenberger's equations, which include a weak
external magnetic field, and provide analytical expressions for the penetration
depth in the various limiting cases. A complete numerical analysis of the
doping and temperature dependence of the London penetration depth reveals the
crucial effect of disorder scattering, which is especially pronounced in the
coexistence phase. The experimental implications of our results are discussed.
