He could have been using 577/450, But I don't think that is what it is, unless the barrel has been recut or relined- 45 would be marked for 52 balls to the pound. 56 ball is .442.

Some thoughts on this. Pure wild thoughts. When measuring bore in these old guns they are talking about the minor or smallest measure in the bore. In standard rifling that would be the Lands. In Henry rifling the bore or minor diameter is the top of the peaks and the center of the flats. The groove or corner of the flats in Henry are major diameters. So if the minor diameter is .442 it is 56 ball. If the groove or major diameter is the standard .005" deep that makes the major diameter of a .442 bore, .452 or 52 balls.

It may appear the barrel has been refinished. All the markings every where else on the gun are crisp and sharp. Barrel proofs are more washed out. I think this is as should be. The gun may have been provided proofed to Purdey in the white and the marks got washed in the finish.

This is very likely as I doubt Breandlin provide this gun to Purdey engraved. I am pretty sure Purdey is responsible for the engraving. They would have polished the gun first and then engraved and finished. Any existing marks would washed.

You do need to do a chamber cast and a bore slugging,

I would slug from the muzzle the first time. As you push the slug down the bore prepare for the slug to go free about 8 inches up from the breech. If it does this is a military barrel.

I do not think the slug will go free in this gun. I do not think this a military barrel.

If it does drop, you need include a section of bore when you chamber cast and measure that for bullet size.

Rifling should be odd number-7 Henry flats and peaks, no lands or groove. It does not take special equipment to measure. It can be measured with your dial caliper. Hold the slug between loose jaws of the caliper. Keeping light thumb pressure on loose jaw, rotate the slug and watch the dial. The high number that repeats as you rotate is your measurement. Do several times.

If you have access to pin gauges, then a .441 pin gauge should run the bore and .442 should not enter. Run=drop in and go through the full length.

Now we need some full length pictures of your gun so we can see this beauty.