We analyze stabilized mixed hp-boundary element methods for frictional contact problems for the Lame equation. The stabilization technique circumvents the discrete inf-sup condition for the mixed problem and thus allows us to use the same mesh and polynomial degree for the primal and dual variables. We prove a priori convergence rates in the case of Tresca friction, using Gauss-Legendre-Lagrange polynomials as test and trial functions for the Lagrange multiplier. Additionally, a residual based a posteriori error estimate for a more general class of discretizations is derived. It in particular applies to discretizations based on Bernstein polynomials for the discrete Lagrange multiplier, which we also analyze. The discretization and the a posteriori error estimate are extended to the case of Coulomb friction. Several numerical experiments underline our theoretical results, demonstrate the behavior of the method and its insensitivity to the scaling and perturbations of the stabilization term.