In this paper, we study the robustness of controllability in the state space $M_{p}=\mathbb{K}^{n}\times L_{p}([-h,0],\mathbb{K}^{n}),$ $1 < p < \infty$, or retarded systems described by linear functional differential equations (FDE) of the form $\dot x(t)=A_{0}x(t) + {\int }_{-h}^{0}d[\eta (\theta )]x(t+\theta)+B_{0}u(t), x(t)\in \mathbb{K}^{n}, $ $u(t)\in \mathbb{K}^{m}, \mathbb{K}=\mathbb{C}$, or $\mathbb R$. Some formulas for estimating and computing the distance to uncontrollability of a controllable FDE system are obtained under the assumption that the system’s matrices $A_0, \eta, B_0$ are subjected to structured perturbations. An example is provided to illustrate the obtained results.