Abstract Background Data privacy is one of the biggest challenges for any organisation which processes personal data, especially in the area of medical research where data include sensitive information about patients and study participants. Sharing of data is therefore problematic, which is at odds with the principle of open data that is so important to the advancement of society and science. Several statistical methods and computational tools have been developed to help data custodians and analysts overcome this challenge. Methods In this paper, we propose a new deterministic approach for anonymising personal data. The method stratifies the underlying data by the categorical variables and re-distributes the continuous variables through a k nearest neighbours based algorithm. Results We demonstrate the use of the deterministic anonymisation on real data, including data from a sample of Titanic passengers, and data from participants in the 1958 Birth Cohort. Conclusions The proposed procedure makes data re-identification difficult while minimising the loss of utility (by preserving the spatial properties of the underlying data); the latter means that informative statistical analysis can still be conducted.