In this paper, $BSE$ properties of some Banach function algebras are studied. We show that Lipschitz algebras $Lip_\alpha(X, d)$ and Dales-Davie algebras $D(X, M)$ are $BSE$-algebras for certain underlying plane sets $X$. Moreover, we investigate $BSE$ properties of certain subalgebras of $Lip_\alpha(X, d)$ such as $Lip_{A}(X, \alpha)$, $Lip^{n}(X, \alpha)$ and $Lip(X, M, \alpha)$. $BSE$ properties of Bloch type spaces $\mathcal{B}_{\alpha}$ and Zygmund type spaces $\mathcal{Z}_{\alpha}$ are also investigated in different cases of $\alpha \in \mathbb{R}$.
