I've recently obtained a model 645 in a gun trade and the trigger, when hammer is cocked, is almost completely against the back of the trigger guard before it releases. The action of the trigger when using it double action seems to be normal. What can be done to correct this?

That's the way it's supposed to function. I suppose you could get it converted to double action only so the trigger would be in the same place all the time. Tarnhelm Police Supply in Concord, NH does the conversions.

If a qualified Gunsmith has determined that other than the tight tolerance you describe all else is perfectly within spec, then I suppose the rear of the trigger could be polished down .010 - .015" but before doing anything, make sure there is no other reason for what you describe.

While the trigger should be close to the trigger guard when the gun is cocked for SA, there should be some clearance and tolerance to make sure the gun goes bang even with some dirt, powder residue and small debris in the trigger guard.