Yes I agree use fine 0000 wire wool and any acid rust remover (Jenolite used to be best but I expect someone in F***ing EU banned it). If this thing is really heavily rusted the idea is to get down to silver metal and have it as shiny as possible even using metal polish. Then you can use a gel method that I describe in the link below.
The secret is to have some
worn out scotchbrite plastic scouring material -
not new out of the box but the stuff that the wife has used for a week in the kitchen sink. Using this slightly rough applicator his will avoid a lot of smears and patches on larger areas. Take heed of the degreasing and the immediate oiling afterwards - it really does help cure the blue.
You will never get a factory finish without using the american browning materials, humidity cabinets and several days processing, but this simple method will give a reasonably good looking job that is much better than red rust. Make sure you seal up the barrel etc.
https://www.youtube.com/edit?video_id=65qCZ9iJl4k