The available published information on the total number of citizenship applications and grants is published as part of the quarterly Immigration Statistics, Citizenship tables, latest edition available at https://www.gov.uk/government/publications/immigration-statistics-year-ending-june-2018/list-of-tables#citizenship
The table below provides figures for all registration applications (entitlement and discretionary) in the last 3 calendar years.
British citizenship applications by broad type
Applications for British
Of which: Applications for registration
Source: Home Office, Migration Border Analysis.
Immigration Statistics year to June 2018 - table cz_01_q.
Applications for British citizenship by the applicant’s age are not routinely published.