The creation of artificial polyglot voices remains a challenging task, despite considerable progress in recent years. This paper investigates self-supervised learning for voice conversion to create native-sounding polyglot voices. We introduce a novel cross-lingual any-to-one voice conversion system that is able to preserve the source accent without the need for multilingual data from the target speaker. In addition, we show a novel cross-lingual fine-tuning strategy that further improves the accent and reduces the training data requirements. Objective and subjective evaluations with English, Spanish, French and Mandarin Chinese confirm that our approach improves on state-of-the-art methods, enhancing the speech intelligibility and overall quality of the converted speech, especially in cross-lingual scenarios. Audio samples are available at: https://giuseppe-ruggiero.github.io/a2o-vc-demo/