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Almost four in five of the public (77 per cent) say they would be willing to allow their medical records to be used in a research study if they were anonymised.

Wellcome Monitor (Wave 3)

Public attitudes to commercial access to health data (Wellcome 2016)

A slight majority (53%) of people would be happy for their data to be used by commercial organisations if it was for research, but most people were extremely wary of insurance and marketing companies accessing even anonymised information

https://wellcome.ac.uk/publicattitudes

Royal Statistical Society

The RSS commissioned two surveys around the theme of data democracy and understanding (2014)

The data trust deficit: Trust in data and attitudes toward data use and data sharing in the UK

A summary, slides, and tables from the research are available

Attitudes to using and linking administrative data for research

ESRC and Office for National Statistics (2013)

Dialogue on Data: Exploring the public’s views on using linked administrative data for research purposes