In short - yes (unless you already have permission to acquire).
Adding an antique firearm to your FAC is a VARIATION to the FAC, so you need a "permission to acquire" slot to allow it to be added. They will want to ensure that you have appropriate storage (once on ticket the gun can no longer be hanging on the wall), demonstrable good reason, and that your total holding does not take you over whatever arbitrary limits you particular force uses. The fact that you already own the gun is immaterial.
As to its history, I presume that you bought the gun as an antique so just tell them what you know about it (when and how you acquired it), or tell them to swivel as this has absolutely no bearing on the variation process and it is none of their business.
I know several collector/shooters who frequently add and remove items in their collection for the occasional shoot - daft innit?
True freedom includes the freedom to make mistakes or do foolish things and bear the consequences.
TANSTAAFL