Not enough battery charge

I replaced the battery one week ago. After several short journeys and around

300 miles, while cruising along the motorway, the new battery ran out of power and I spluttered to a halt. The alternator light has not even flickered while driving.

My understanding is that a battery can drive a car for maybe 30 minutes without receiving any charge. Although the new battery was a bit more powerful than needed (60 Ah for a 2.0i Cavalier) and it was fully charged before fitting, I can't believe it could have lasted so long without getting any charge.

I've checked some wires. The battery terminals were all clean, as was the red connection from the alternator. The alternator earth was a little dirty and has now been cleaned.

Is it possible for an alternator to give some charge, but not enough to the battery? Should I replace the alternator? What are the chances that the alternator earth was the problem? How can I check the efficiency of the alternator with a voltmeter?

Thanks in advance for any thoughts.