My two cents: I guess that would 2 shillings hunh?

Everyone has hit the most common causes, cleaning, bedding, etc...

Try checking the screws with a pound inch torque wrench. Verify that the screws are tight and that contact with your wood has not changed. This can be caused by a change in contact pressure due to ambient conditions, e.g. temperature and humidity. Some one said try shims. business cards will really quickly show if more or less pressure has any affect on precision. Experiment, it is cheaper than the alternative.

The last part where you describe the "shadow" in the throat area, sounds like throat erosion caused by micro stress corrosion fractures in the surface of the steel. Refer to technical papers by Lazzeroni et al for more detailed looks into this phenomenom. It cuases a rough cracked surface that will eventually remove the rifling in the leade/throat area of a barrel. In America the love of Big magnums (and yes I have one too!!!) has exascerbated this problem. A mild round like the .303 will cause this after a lot of rounds. It can lead to reduced accuracy usually by allowing the bullet, when it finally does enter the lands, to do so at an angle, therefore reducing precision. On the bright side though you are fortunate that most precision is affected by the crown of the barrel rather than the throat. Check the tech papers by Lazzeroni for the details. Unfortunately it is a barrel replacement type problem. On many sporter weight barrel it can be corrected by cutting an inch of the chamber end and re-reaming, or chambering for a longer round. That will not work on an issue barrel. sorry.

Check the shims first, if no luck; bore scope the bore and see if it looks like dessert floor, if so: stress corrosion fractures. It is obviously bad enough to affect accuracy, so barrel replacement would be in order. Here in the USA 2 groove Bbls are all over. Even complete rifles are only $250. Part it out and some one who needs other Savage parts will be thankful.

Good luck.