Medical statisticians are mainly employed by most medical schools and universities, and by public sector research organizations (such as the Health Protection Agency and the World Health Organization). If you do not wish to spend your whole career in the academic sector, it is usually possible to switch to the private sector (for example the pharmaceutical industry) or the civil service after a few years.
Advertisements for medical statisticians appear in several places, including daily newspapers such as The Times and The Guardian, RSSeNews, electronic mailing lists (such as AllStat and Public-health), websites at medical schools and other general websites such as www.jobs.ac.uk .
Job titles are not necessarily “Medical Statistician”. There are, for example, non-clinical research and lecturer posts in Epidemiology, Public Health or Health Services Research.