What you likely saw is an additional safety intercept or locking catch, sometimes added on high-end British doubles. On classic Holland & Holland rifles, the normal top-slide safety already blocks the sears, and many also include internal intercepting safeties that prevent discharge unless the trigger is deliberately pulled.
That “swinging” secondary piece is usually an extra manual lock—either a bespoke modification or a period feature—meant to physically secure the main safety from being moved accidentally, especially in dangerous game conditions. Not common, but very much in line with H&H’s emphasis on redundancy and absolute safety.
