Population Estimates LA & Ward

ENGLAND & WALES
MYEs for 2019 were fully published 24th June May, 2020 and are available here.
ONS also publish various analysis tools and detailed background data:
Quality Assurance (QA) Pack comparing MYEs to Admin Data
Interactive Analysis Tool
Detailed Components of Change (MYEB2) 2001 to 2019
(Zip file with 2019 & 2020 LA Geography in csv)

Previous set of MYEs for England & Wales
Mid 2018 here.
Mid 2017 here
Mid 2016 (Revised May 2018) here. Original (June 2017) here.

For a series of links to information for 2017 MYEs (Awaiting update for 2018 and 2019 MYEs) and tools on how to analyse the data for your area, see the following which was complied by ONS and I have some extra links that may also be of use Population quality links ONS Nov 2018

If your Wards have changed, ONS will start publishing Ward level Population Estimates (and other statistics including Births and Deaths)  in the year following introduction. So if your Wards came into effect in May 2019, then ONS will publish Ward Population Estimates for Mid 2019 (and Mid 2018) in November 2020.

If you would like Population Estimates for your new Wards for Mid 2019 before then, these can be calculated now and I can provide an Access database that will allow you to create your own age groups – it can also be adapted to allow any groups of Output Areas (or parts thereof)  to create bespoke area or communities.

For England & Wales the latest Small Area (including Wards) ONS figures,
ONS Small Area Population Estimates Mid 2018 (Published Oct 2019)
ONS Small Area Population Estimates Mid 2017 (Published Oct 2018)

Also available,
Mid 2018 by MSOA, LSOA and OA
Mid 2017 by MSOA, LSOA and OA

SCOTLAND 
MYEs for Council Areas Mid 2019 (Published April 2020)
MYEs for Scottish Data Zones Mid 2019 (Published Aug 2020)

Previous Sets:
MYEs for Council Areas 2018 (Published April 2019)
Scottish Data Zones Mid 2018 (Published Nov 2018)
Mid-2017 Population Estimates for Settlements and Localities in Scotland (Published June 2018)

NORTHERN IRELAND
For Northern Ireland figures, 2019 MYEs are available here
Super Output Areas (SOAs) and former Electoral Wards, Mid 2019 
Small Areas & Neighbourhoods Mid 2018  (Published Nov 2019)