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PHE Data and analysis tools - A whole range of statistical data on a variety of health topics arranged in an A-Z format by Public Health England
For UK social as well as health statistics, try the government Statistics website
The ONS (Office for National Statistics) is the UK's national institute of statistics and provides population, health, employment and many other national statistics.
UK Data Service collection includes major UK government-sponsored surveys, cross-national surveys, longitudinal studies, UK census data, international aggregate, business data, and qualitative data.
NHS Digital includes a section on Health data and statistics. For statistics by health condition or population (e.g. maternal or child health) look at the Publications by Topic page.
If you're looking for which conditions are most prevalent in a census ward/small area then the Health Conditions Atlas developed by the Small Area Health Statistics Unit might be useful
Health Profiles provide a snapshot overview of health for each local authority in England. You can search by town, postcode or local authority.
For differences in life expectancy and healthy life expectancy between communities try the Public Health Outcomes Framework
To view a map and statistical data by ward, e.g. Blackbird Leys, try PHE local health statistics
Find the NICE Clinical Knowledge Summary for the condition you're interested in and then look under Background Information at the Prevalence page for statistics. A selection of both UK and worldwide data is available.
If you're looking for cancer statistics, you could try
NCRAS - the National Cancer Registration and Analysis Service Cancer statistics for the UK - on the Cancer Research UK website
Data on UK smoking habits and related health problems can be found on the Public Health England Local Tobacco Control Profiles
Natsal - The National Survey of Sexual Attitudes and Lifestyles is carried out in the UK once every 10 years. You can find details of the survey methodology and links to reports of the findings (published in journals e.g. BMJ and The Lancet) on their website. If you're looking for sexual behaviour in older people, it's worth noting that the earlier surveys stopped at age 44 and 59, only the latest survey goes up to age 74.
The World Health Organization's Global Health Observatory is a gateway to global health-related statistics.
Health Statistics User Group - sign up to keep up to date with Health Service Statistics
The Library webpage on Statistics contains some more links to UK and international statistics.