I don't know how familiar you are with "British" guns in general, but I hope so! I had a number of arms including a 303 SMLE and a 303 No4. I have had to sell the SMLE as with the mid-sight as fitted I could only see that blurred. Certainly not enough to shoot the rifle with as much consistent shot placement, and so accuracy, as I once could.

I have two fine BRNO ZKK rifles. One a 600 in .243 and the other a 601 in .270. These are early models with both a mid-sight on the barrel and a receiver mounted peep, or aperture, sight, on the rear receiver ring. Again I fold down the mid-sight and use the receiver sight.

The No4 is different. It has a rear mounted aperture sight mounted on what would be the rear "receiver" ring and a Mauser type action. With this I can still shoot. The eye fids the hole and if it is blurred it doesn't matter...indeed that is how it should be seen. A "ghost" ring as some would call it, I think.

I can also get good sight pictures with a Greener GP gun. That has a large "notch" on the front of its Martini action receiver. Again a little blurred but I can still get a good consistent sight picture.

My advice would be to consider a flip-up aperture sight on the tang of you double. Indeed I believe that one English maker actually had a patent for such a sight in the top lever itself. Or...to perhaps move the mid-sight on the barrel nearer the eye?

You could experiment with a piece of card stuck to the top rid or perhaps some sort or sight that could had an extended base to bring the leaf back nearer to the breech.

The simple solution...not the cheapest...would be a 1x or 1.5x telescopic sight! Another solution might be to enlarge the aperture on your mid-sight so that it is very large and like a half-moon. So that it becomes, in effect, like the bottom half of a "ghost" ring. Again experiment with a piece of card glued on.

I am, however, certain that Holland's or Paul Roberts (once Rigby now Jeffrey) would not be unfamiliar with your problem...and may have a solution already tried and tested.