The iron depends on how far back you go and the vext question, when did they start puddling?

Dud Dudley was producing many grades of cast iron some of which lent themselves to 'fining'. But did he puddle?

You can refine iron by literally bashing the cr@p out of it. Presumably how they made currency bars, cast iron being no good for sword or plough share.

Puddling produces almost pure iron with a slag inclusion, working the puddled iron so the slag becomes long and thin and not localised makes wrought iron which is perfect for the smithy.

The Enfields went on one stage being made from Marshall's iron, almost certainly crucible steel. Marshalls factory in B'ham has been excavated. Crucible steel involves taking puddled iron rods, case hardening them to add carbon then remelting to even the carbon content through the mix. Pre-Bessemer the remelting was exceedingly tricky because it is only the impurities that get the melting point down. Crucible steel made excellent razors, no imperfections to interrupt a fine edge.

Then came cartridge guns and I completely lose interest, quite understand why you might insist on proofing and never trust that new fangled stuff.

Personally I like damascus iron, only problem with damascus is that it doesn't take to rifling very well. That's why my deer rifle has a damascus outer over a tape wound core