Within the UK
ONS use GP Patient records to update their Migration estimates of within UK moves. They also use Student Address data from the Higher Education Statistics Agency to adjust the estimates.
Matrix of Moves between Local Authorities in England & Wales (Northern Ireland and Scotland shown as entire countries only)
Figures are published annually and since 2011, are in the form of single year estimates by gender by Local Authority.
The data for moves in the year to Mid 2018 are available in two parts
Part 1 and Part 2 but is not user friendly. If you are interested in a database with all the data from 20012 to 2018 (7 million+ records), get in touch.
If you would like the figures aggregated for your Local Authority/Authorities, I can supply an Excel spreadsheet that will allow you to cross-tabulate age groups and gender for the years from Mid 2012 to Mid 2018.
ONS publish a Local Authority Migration Indicator Tool that shows trends in admin data sources linked to international migration e.g. NINO, Flag 4, Short Term and Long Term Estimates, turnover and rates. It covers the years from 2004 to 2018. See Migration Tool.
The latest quarterly estimates (Year to June 2019) for International Migration to and from the UK can be found here.
Short Term International Migration
Figures for Local Authorities for Mid 2017 (published 24/5/19) available here.