If you need to know the weather, go to the Meteorological Office site. The latest infrared and visible-light satellite pictures, regional and coastal forecasts, and even gale warnings nestle beside details of how the Met Office does the forecasting. The Financial Times site features information from the newspaper, plus other financial and markets information. There's also a good archive of previous articles.
Access is free, but registration is required.
Basic timetabling information is this Web site's forte, and this data is often all you need. It'll tell you about catering, which class of travel is available, and whether you need to reserve. Travelling to Paris and Brussels got a lot easier with the launch of the Eurostar service. The BSI site can't, by any stretch of the imagination, be construed as exciting. However, if you need standards reference material it's essential, and forms a concise entry point for those unfamiliar with the activities of the British Standards Institute.