It sounds likely that the coolant level is low, or that the coolant level sensor is faulty. The red light flashes under three different (normal) circumstances.
1. On starting the ignition for a few seconds or so.
2. If the coolant level is low.
3. If the coolant temperature gets too high - assuming that the gauge/indicator and the temp sensor are working correctly this would normally happen after the needle on the coolant gauge gets about 3/4's of the way up.
There's no way your engine will be overheating after only 10 minutes so I would expect that the light is indicating a low coolant level.
What you need to do is check the level in the expansion tank. This is the tank that is located inside the engine bay, NOT the one behind the registration plate flap. The level in the expansion tank should be right to the top, so it's spilling out the top when you screw the cap back on. Top up with distilled water if possible and use some antifreeze too if the level is extremely low - you don't want to dilute the antifreeze level too much. However be careful what antifreeze you use as it can be a bit of a can of worms. Have a look at the WIKI for advice.
If the level was fine to begin with, or if topping up has no effect on the light problem, then it is possible that the coolant level sensor is buggered or maybe just dirty. The sensor is screwed into the top of the expansion tank. Unscrew it and give the two prongs a clean with a tissue or something - they can get a bit grubby over time. If this still doesn't work then consider replacing the sensor itself, they are only a few quid from brickwerks and very easy to fit.
Let us know how you get on.
