If you are trying to find out about news events as they happen, or about things that have just happened, search engines and directories are a bad idea. The indexes they use can be months out of date. That has led to the development of "breaking news" sites that specialise in relaying news as it happens.
Introducing the news aggregators
The sites mentioned here are not broadcasters or newspapers. You can find more about those sites on the news organisations page. The sites here are "news aggregators". They gather together reporting that is actually written by other people.
One useful British-based sites is NewsNow. It not only puts out current headlines, it allows you to search the headlines of its output for the last 30 days. It claims to have 3000 sources and is updated every 5 minutes. It has a strong business and technology bias, but is also keen on sport.
Looking for world news
Once you get away from British sites, there is plenty of choice. RocketNews has a simple front page that tells you exactly what it does. Type in your search terms and it will find relevant news stories from around the world for the last five days. It also searches weblogs, audio, and video.
Google, inevitably, has a Google News and Google News UK pages. They offer a frontpage of headlines, and a search box. The good news is that you can use some of Google's syntax tricks to restrict the searches. Google News's special trick is that, like the main site, things come to the top through popularity rather than because an editor put them there. Or so Google claims.
Most of these news sites tend to see world events from a US perspective. HeadlineSpot includes links to all sorts of American columnists and commentators as well as straight reporting, listed by source rather than headline. I also like comes from NewsHub, which offers a page of headlines and a search box. It is updated every 15 minutes. Because these sites link to the BBC and other British news organisations, the basics of UK stories can usually be found.