I have a Savage No 4 Mk 1 .303 British Enfield.  The firing pin retaining screw is solidly stuck.  Not corroded by external inspection, and the rifle fires properly, but I cannot get the firing pin retaining screw out to clean the firing pin.  I have used Kroil to no avail.  Any suggestions?

Assuming you mean the screw on the rear of the cocking piece that prevents the firing pin from being unscrewed???

About all you can do is mill the head of the screw off.
One the head is off, you can use the tubular wrench to unscrew the firing pin.
With the bolt apart you can then extract the threaded shank of the screw.

I don't recommend attempting to drill the head of the retainer screw off.  Drill presses just don't have the precision needed to cut the head off without drifting off center.
With a milling machine and milling drill NOT a standard drill you can "bump" the milling machine over to keep it centered, and the mill drill won't flex and bend like a standard drill.

Another option before removing the screw head.
Lock up the bolt in a drill press with the bolt body at 90 degrees to the chuck.  
UNPLUG the drill and pull the belt off the pulley.

Chuck a Brownell's Magna-Tip screwdriver bit that's a perfect fit in the screw slot in the chuck and pull it down into the screw slot.
Turn the chuck using a rod as a handle while pulling the chuck firmly down into the slot.
The gunsmith driver bit and the down pressure will prevent the driver from camming up out of the slot.

This is a basic gunsmith method of removing stuck screws.
Either the screw will come out or 1/2 of the head or the entire head will break off, at which point you're back to the milling machine.