We prove that if 𝔠 is not a Kunen cardinal, then there is a uniform Eberlein compact space K such that the Banach space C(K) does not embed isometrically into $ℓ_∞/c₀$. We prove a similar result for isomorphic embeddings. Our arguments are minor modifications of the proofs of analogous results for Corson compacta obtained by S. Todorčević. We also construct a consistent example of a uniform Eberlein compactum whose space of continuous functions embeds isomorphically into $ℓ_∞/c₀$, but fails to embed isometrically. As far as we know it is the first example of this kind.