you should jump start the car and then measure the voltage across the battery with a multimeter. if must be 14v minimum, 14.4v should be expected when the car is running with no electrical accessories turned on. a voltage of less then 14v would suggest a faulty alternator, voltage regulator, alternator belt snapped or wiring fault in the charging circuit.
if the battery was at fault you would have noticed the car stuggling to start over the past few weeks, the problem gets worse and worse as the battery dies, a sudden problem like yours is less likely to be the battery.
if the engine isnt even trying to turn when you start it with the key it could be the starter motor, especially if the engine doesn't even try to start at all. starter motors can fail suddenly without warning, usually due to dodgy wiring.
an alternator costs £15-20 if you remove it yourself from a scrap yard, and its the same for a starter motor, but i doubt either of them will actually need changing. i'd take a mistic meg type guess its a bad connection on a wire