During the COVID-19 pandemic, digital contact-tracing has been employed in many countries to monitor and manage the spread of the disease. However, to be effective such a system must be adopted by a substantial proportion of the population; therefore, public trust plays a key role. This paper examines the NHS COVID-19 smartphone app, the digital contact-tracing solution in the UK. A series of interviews were carried out prior to the app's release (n = 12) and a large scale survey examining attitudes towards the app (n = 1,001) was carried out after release. Extending previous work reporting high level attitudes towards the app, this paper shows that prevailing negative attitudes prior to release persisted, and affected the subsequent use of the app. They also show significant relationships between trust, app features, and the wider social and societal context. There is lower trust amongst non-users of the app and trust correlates to many other aspects of the app, a lack of trust could hinder adoption and effectiveness of digital contact-tracing. The design of technology requiring wide uptake, e.g., for public health, should embed considerations of the complexities of trust and the context in which the technology will be used.