Large language models (LLMs) promise to automate one of higher education's most resource-intensive activities: assessing student writing. Existing evaluations are typically limited to a single model, a single prompt and a single institution. Using 761 undergraduate psychology assignments from three UK universities, we evaluated three frontier LLMs, individually and in ensemble, on accuracy, prompt sensitivity, error independence, generalisability and evidential basis. Agreement between human and machine marks varied widely, with no model or prompt optimal across institutions. All models compressed marks towards a common central tendency, overvaluing the weakest assignments and undervaluing the strongest. Because this error was shared, ensembling failed to remove it. Machine marks also rewarded linguistic features more strongly than human marks. Since human-machine agreement was a joint product of model, prompt and institution, we conclude that current LLMs lack evaluative capacity transferable across contexts, and that single-context validation overstates readiness for deployment.

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