Regarding the shooting of jacketed bullets in these old rifles, I believe the Woodleigh 440-grainers ( and the 650gr .577s) have relatively thin jackets being designed for black powder barrels, and are marked B.P. on the box.
I have absolutely no hesitation in shooting them in my BP doubles.
ie .500/.450 Tolley; .577/.500 No.2 Rodda; 20-bore/.577 Alex Henry; .577 x 2 3/4 Army & Navy.

...but erring on the side of caution will never be criticized here!