I came across this thread because I was looking for 2021 ward results, I'm not sure if you're still interested in this.
There's a downloadable spreadsheet with all the ward results for 2016 here (although I'm not sure its exactly what you wanted):
https://data.london.gov.uk/dataset/london-elections-results-2016-wards-boroughs-constituencyThere's also this interactive map which has 2004, 2008 and 2012, but not 2016 unfortunately:
http://londondatastore-upload.s3.amazonaws.com/instant-atlas/gla-elections-const-2000-12-html5/atlas.html