The National Census was first carried out in England in 1801, and was planned to be repeated every ten years. From 1841 onwards the census data was recorded in enumeration books in a standardised format, and it is these records that are often quoted and reviewed. More details of the process are at the National Archives Website here.
Census Records still exist for Church Lawford for 1801, and for both villages from 1841 to 1921. The records for 1931 were accidentally destroyed during the Second World War, and no census was taken in 1941. The Census Data for 1951 onwards is still kept private, and will not be available for public viewing until 100 years after the census date.
The complete set of Census information for the two Villages currently available can be accessed via the links below