The 2020 Coronavirus pandemic is a major international public health challenge.  Governments have taken public health protection measures to reduce the spread of the virus through non-pharmalogical measures. The impact of the pandemic and the public health response on individual and population mental health is unknown.  We used Google Trends data (1 Jan 2020 -  30 Mar 2020) to investigate the impact of the pandemic and government measures to curb it on people's concerns, as indexed by changes in search frequency for topics indicating mental distress, social and economic stressors and mental health treatment-seeking. We explored the changes of key topics in Google trends in Italy, Spain, USA, UK, and Worldwide in relation to sentinel events during the pandemic. Globally there appears to be significant concerns over the financial and work-related consequences of the pandemic, with some evidence that levels of fear are rising. Conversely relative searching for topics related to depression and suicide fell after the pandemic was announced, with some evidence that searches for the latter have risen recently. Concerns over education and access to medication appear to be particular social stressors. Whilst searches for face-to-face treatments have declined, those for self-care have risen. Monitoring Google trends shows promise as a means of tracking changing public concerns. In weeks to come it may enable policy makers to assess the impact of their interventions including those aiming to limit negative consequences, such as government funded financial safety nets.