This article asks whether the necessity of many public services results in a readiness of individuals to share personal data, and thus sacrifice a certain level of privacy, in connection with their provision. It will explore the value of privacy in the context of the on-going debates around personal data sharing, with particular focus on the public sector in England, using the UK government’s care.data project as an example. The impact on trust relations between the government, the National Health Service (NHS) and the citizen will be considered. The importance of anonymisation of personal data as a method of minimising privacy risks and increasing trust will be discussed. Using the results of the author’s exploratory empirical study into attitudes to sharing personal data with the public sector, the article will suggest that the benefits-versus-costs privacy problem is particularly significant in relation to data sharing projects in the public sector. The lack of definitive answers in relation to the risk of re-identification contributes to the problem. Finally, the article will suggest that future work may wish to investigate how trust in, and acceptance of, data sharing initiatives could be improved by a bottom-up institution-led approach.