The Public Records Office (PRO; also called the GRO or General Register Office) keeps indexes to the civil registrations (starting in July 1837) of births, marriages, and deaths in England. (These indexes were formerly kept at a place called St. Catherine's House, and are still commonly referred to as St. Catherine's indexes.) These indexes are available at many libraries in England, on microfilm from the LDS, and from several fee-based online search services, including called FindMyPast.com.
The indexes tell when and where the event occurred, but do not give details. Here is a sample of a birth index - the fields are Surname, Given Name of Child, Registration District, Volume, Page:

Once you have an index entry you think is the person you're looking for, proceed to ordering a certificate.