The Gazettes

Either it changed recently or I`m way behind the times. The collection of the London, Edinburgh and Belfast Gazettes that used to be at Gazettes Onone is now at The Gazette.
All the same information is still there, back 350 years, but you select London, Edinburgh or Belfast through a filter on the results.
There are a few short explanatory videos, with recognition that genealogists are a major client, at www.thegazette.co.uk/videos
The Republic of Ireland has its own gazette Iris Oifigiúil published since January 1922, but the online archive only goes back to 2002.
According to information at http://timeline.ie/dublin-gazette-iris-oifigiuil/ at the website of the Oireachtas Library you can download pdf copies of the predecessor Dublin Gazette from 1750 to 1809.  Each download covers a decade of the publication, which can then be searched for any term you are looking for.