Emerging optical imaging techniques such as hyperspectral imaging (HSI) provide a promising non-invasive solution for intraoperative tissue characterisation with the potential to provide rich tissue-differentiation information over the entire surgical field. Neuro-oncology surgery would especially benefit from detailed real-time in vivo tissue characterisation, improving the accuracy with which boundaries of safe surgical resection are delineated and thereby improving patient outcomes. Current systems are limited by challenges with processing the HSI data because of incomplete characterisation of the optical properties of tissue across the complete visible and near-infrared wavelength spectrum. In this study, we characterised the optical properties of various freshly-excised brain tumours and normal cadaveric human brain tissue using a dual-beam integrating sphere spectrophotometer and the inverse adding-doubling technique. We adapted an integrating sphere to analyse 2 mm-thick tissue samples measuring 4-7 mm in diameter and validated the experimental setup with a tissue-mimicking optical phantom. We investigated the different spectral signatures of freshly-excised tumour tissues including pituitary adenoma, meningioma and vestibular schwannoma and compared these to normal grey and white matter, pons, pituitary, dura and cranial nerve tissues across the wavelength range of 400-1800 nm. It was found that brain and tumour tissues could be differentiated by their optical properties but the freezing process did alter the tissues' relative absorption and reduced scattering coefficients. In this work, we have demonstrated a method to characterise the optical properties of small human brain and tumour specimens that may be used as a reference dataset for developing optical imaging techniques.