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.