A good website for trying to see how populations changed in Britain is the Histpop website. There is a lot of detail, down to parish level. Genealogists of course know about the 1841 census, and the ones every 10 years after that, but the censuses before that are very good if you just want to know numbers, not names. For Britain this started in 1801, for Ireland unfortunately in 1821, which would have been after some pretty big emigrations.
I made the following summary for Wales, Scotland and England. It will be interesting to keep track of this table, comparing it to our own numbers of participants for each county.