Since removing the timing cover on a TR3 involves a lot of labor, I would want to be absolutely sure the tensioner was the source of the noise. Start by removing or loosening the fan belt and start the engine. This will eliminate the gen. or water pump as the culprit.
Two days ago, I replaced the timing cover seal on my TR6 and upon starting the engine there was a noise similar to the one you describe. After recovering from despair and a change of underwear, my first thought was the timing chain or tensioner, then I decided to eliminate any other cause. I loosened the fan belt to the point that the water pump and alt. wasn't turning and the noise went away. Close examination of the alt. fan showed that it was slightly bent, contacting the alt. frame and producing the noise. In your case, water pump bearings, gen. bearings, or the gen. fan could produce the noise.
The message of this diatribe is to eliminate all of the easy causes of the noise before tackling the labor intensive ones. Good luck.
Berry