Cryptic crossword clues are challenging linguistic reasoning puzzles, with fresh, real-world test cases published daily in major newspapers globally. Unlike standard crosswords, cryptic clues uniquely combine a ‘definition’ with intricate ‘wordplay’ – a logical puzzle embedded in language – designed to prove each answer’s correctness through reasoning alone, independent of grid context. This work describes an open-licensed, LLM-driven system for automated cryptic crossword solving which generates: (i) answer hypotheses and wordplay explanations; and (ii) code-based verification of the proposed reasoning, ensuring solution validity. Critically, our system achieves state-of-the-art performance on the challenging Cryptonite dataset, comprising cryptic clues from prestigious UK newspapers like The Times and The Telegraph. Furthermore, by expressing each verified solution and its reasoning in executable Python code, our system offers unprecedented interpretability, allowing for detailed inspection and analysis of the automated cryptic crossword solving process.