Genomic medicine has captured the imaginations of policymakers and medical scientists keen to harness its health and economic potentials. In 2012, the UK government launched the 100,000 Genomes Project to sequence the genomes of British National Health Service (NHS) patients, laying the ground for mainstreaming genomic medicine in the NHS and developing the UK’s genomics industry. However, the recent research and reports from national bodies monitoring genomic medicine's roll‐out suggest both ethical and practical challenges for health‐care professionals. Against this backdrop, this paper, drawing on qualitative research interviews with general practitioners (GPs) and documentary analysis of policy, explores GPs’ views on mainstreaming genomic medicine in the NHS and implications for their practice. Analysing the NHS’s genomic medicine agenda as a ‘sociotechnical imaginary’, we demonstrate that whilst sociotechnical imaginaries are construed as collectively shared understandings of the future, official visions of genomic medicine diverge from those at the forefront of health‐care service delivery. Whilst policy discourse evokes hope and transformation of health care, some GPs see technology in formation, an unattainable ‘utopia’, with no relevance to their everyday clinical practice. Finding space for genomics requires bridging the gap between ‘work as imagined’ at the policy level and ‘work as done’ in health‐care delivery.