One other thing to factor in, is whether or not your bullets have solid or hollow bases.
I haven't had any experience with "triple 7" but black powder does like to be compressed and abhors voids.
If your Google Fu is good, there is an article in Handloader No 144/1990, on page 32, by Gil Sengel on "practical loads for the 455 Webly Revolver"
It has smokeless powder loads for the 250 grain "flat base bullets" used RED DOT 3.7 grains/Green Dot 4.6 grains/Unique 5.2 grains for appx 630fps, using MkII cases.
MkII cases are .760 OAL.
MkI cases are .870 OAL
Charge weights are slightly different.
Ken Waters Pet Loads lists HP38 5.7 grains/ ww231 6.0grains
The bore diameter on these old revolvers vary quite a bit from median spec. That's one of the reasons for the "hollow base" bullets. The skirts expand/swage down to fill the grooves.
Some folks like to fill the hollow base with "Bondo" to eliminate the air space and assist in expanding the skirts under the BP pressures.
As mentioned above, condition of the revolver is a concern. Your pistol appears to have been refinished and shows some pitting.
Still, those pistols are quite strong for the period and very nice to shoot. Enjoy.
Black Powder loads for the 455 Webley MKII can be tricky because it's the small case.
I use 15.0 grains of FFFG over magnum primers.
I also show an old load for Pyrodex, which I don't know how close it is to 777, 20.0 grains but it was used with MkI cases.
Hope this helps a bit.