A wet plate car battery has a nominal voltage of 13.8 volts when fully charged. Each of the 6 cells that go to make it up produces 2.2 volts.
Your batteries inability to hold a full charge could be attributed to age. Although you say this one is less than a year old. Check the electrolyte if its not a fully sealed type.
A car battery will last for 3-4 years under normal conditions depending on the amount of daily use. But if you are doing a lot of short trips with lights, heater, screen heater and hammering it with a big sound system, this will drop dramatically.
Simply measuring the voltage across the terminals will tell you very little, you need to have a drop test done or get a specialist to check it on a battery diagnostic tool.
Don’t use Halfords, they usually haven’t got a clue, go to LSUK (used to be Lucas) they are proper auto-electricians.
If your alternator is managing to put any charge into the battery, chances are it is working correctly. It is unusual, but not unheard of, for an alternators performance to drop off, they normally work or they don’t.
Give it a good charge (12 hours) and see if things improve or If you have access to another car, swap the batteries for a couple of days and see what happens.
You may have to bite the bullet and replace it, (or take it back under warranty) but it’s worth checking it first before you go looking for an expensive alternator.