The purpose of this study is to investigate the effect of adding whole brain radiotherapy after surgery and/or stereotactic irradiation (SI) on the development of further brain metastases (cancer spread to the brain) in participants with melanoma. Stereotactic irradiation is a form of radiotherapy that is highly focused. This enables radiotherapy to be given to a small volume without damaging nearby structures that may be sensitive to radiation. It can be given to multiple tumour lesions in the brain in the same sitting. It is only available in some centres. It is usually reserved for lesions that are difficult to operate on because they are deep inside the brain or close to important structures that could be compromised by neurosurgery. The results of SI for small lesions (usually less than 3 cm in diameter) are similar to surgery. It can be given alone or added to surgery when the neurosurgeon thinks that removal of the tumour by surgery has not been adequate. In some hospitals, whole brain radiotherapy is already the standard treatment, but in other hospitals it is not. It is not known for certain whether the benefits of using whole brain radiotherapy (i.e. prevention of new tumours) outweigh the risks of having this treatment. This study will look at the effect of whole brain radiotherapy on overall survival and quality of life.