Rail investigators are looking into claims a train broke the speed limit on a restricted piece of track in Powys (link below.)
http://news.bbc.co.uk/1/hi/wales/mid/7015809.stm

The Aberystwyth to Birmingham Arriva Trains service is said to have reached 80mph (128km/h) between Newtown and Caersws in a 20mph (32km/h) zone.

Yes, Graham. Speeding over a temporary speed limit, even by that margin, is unlikely to be 'dangerous' as it's probably a limit put in place due to worn out/recently replaced track and one train going over it at the normal speed would not be a problem. A permanent speed restriction of 20, say over points, or very severe track curvature would be a different matter - the train would not have remained on the track at that speed!

For each temporary speed restriction the driver receives a lineside warning which is set at the Service Braking Distance for that route (i.e. the distance it would take for the train with the least braking performance to adequately slow down). Additionally where Automatic Train Protection (ATP) is fitted the train's speed is monitored by the on-board computer to ensure the driver slows the train down enough.

However, as with anything that has a human element attached, mistakes sometimes happen. For example, if it is a 20mph restriction on a 125mph section of track the warning board will obviously be some distance from the actual restriction and elements such as stations in-between, and other distractions means it is possible for the driver to forget. It is, However, quite rare.