It's rare but possible. There's a lame YTer called Will Tennyson, he did a DNA test on his channel and it came back 100% white, something like 80% English. He has black hair and eyes.
I've met a British girl with black hair and eyes, and she's definitely pure. It's simply a variant.
I would suspect that anyone from the British isles with black hair and brown eyes actually has Spanish/Berber admixture, like the so-called "black Irish". The reason they show up as "100% British" in DNA tests is that the results for those tests are based on how reference subjects self-identified. For example, if a "black Irish" person self-identified as pure Irish in the test's reference matrix, then any "black Irish" person who takes the test is going to get back a pure Irish result.
I've met a British girl with black hair and eyes, and she's definitely pure. It's simply a variant.