The Home Office publishes data on Family Reunion in the ‘Immigration Statistics Quarterly Release’. https://www.gov.uk/government/collections/immigration-statistics-quarterly-release
Data on grants of Family Reunion visas by nationality are published in table Fam_D01 of the asylum and resettlement detailed datasets. Data on applications and outcomes of Family Reunion visas by nationality are included in the ‘Family: other’ visa subgroup in tables Vis_D01 and Vis_D02 of the https://www.gov.uk/government/statistical-data-sets/managed-migration-datasets#entry-clearance-visas-granted-outside-the-uk
Although ‘family reunion’ visas are not separately available, the vast majority of ‘Family: other’ visas are family reunion.
Information on how to use the dataset can be found in the ‘Notes’ page of the workbook. The latest data relates to year ending September 2019. Additionally, the Home Office publishes a high-level overview of the data in the asylum summary tables and entry clearance summary tables. The ‘contents’ sheet contains an overview of all available data on asylum and entry clearance visas.
Information on future Home Office statistical release dates can be found in the ‘Research and statistics calendar’. https://www.gov.uk/search/research-and-statistics?keywords=immigration&content_store_document_type=upcoming_statistics&organisations%5B%5D=home-office&order=relevance