Maybe..
When you say the battery stutters, do you mean it doesn't turn the engine over? Whether the engine starts or not the batter should be able to spin it over quickly.
If it just clunks and makes a groaning noise, then the battery or starter motor would seem to be not in good shape (though "battery" may end up being the alternator not actually charging it).
If you think the battery is flat, try charging it and then see if that makes the engine turn over more quickly. If it then goes flat, that's a battery or alternator problem.
When the engine is running at a fast tickover, the voltage across the battery terminals (you'll need a voltmeter) should be around 14.5V if the alternator is okay.
First thing in the morning with the engine off, the voltage should be 12.6V if the battery is holding its charge.
More likely though the battery and alternator are fine but the beast is just reluctant to start.
I think it's the coils. Take a spare spark plug and one at a time, connect the HT leads from each cylinder to it, rest it on the engine to earth it, and try to start the engine. Do it in a dark place.. and don't hold the HT lead, or take the plug away from the engine.. it must touch all the time or you'll fry the ECU.
You should see the plug sparking. If it does, repeat if for each cylinder in turn until you find one (or two) that don't work. Follow the HT lead back to the coil (under the black plastic cover, on the right of the engine) and see which coil its connected to. There's two coils.. each one feeds two cylinders. If the coil is duff.. get a new one.. £40 or thereabouts.
Ralf S.