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In this paper we study existence and uniqueness of solutions for the Hammerstein equation $$u\left(x\right)=v\left(x\right)+\lambda {\int }_{I_a^b}K(x,y)f(y,u\left(y\right))dy$$ in the space of function of bounded total $\varphi$-variation in the sense of Hardy-Vitali-Tonelli, where $\lambda \in ℝ$, $K:I_a^b\times I_a^b⟶ℝ$ and $f:I_a^b\times ℝ⟶ℝ$ are suitable functions. The existence and uniqueness of solutions are proved by means of the Leray-Schauder nonlinear alternative and the Banach contraction mapping principle.