Mine is also a 2000 Classic, and I had a similar problem the other night. The car has been sitting for a couple of days after a wet drive. When I went out for a drive, it was stuttering quite a bit till it was warm.
I've had this problem in various cars, and I'm pretty sure it's down to the leads. This would tie in with it working properly for a short period after you fitted new plugs, as you would have "refreshed" the dodgy connection on a lead when you removed them to change the plugs. Best way to check is open the bonnet when you feel it happening, at night in the dark, and look for sparks. Usually where the lead plugs into the coil pack.
I've not replaced mine yet, too cold and skint at the moment, lol.