How to eradicate Bracken
 

Hi there, I have been assigned to eradicate a large area with bracken (and a little J knotweed) from a large veg bed that hasn't been used in a few years, please see image. The owners have placed black polythene (which has now very worn) and they wish to have it replaced (already have new roll of polythene), now my question is this, I do plan on putting new plastic over the site but how would be best to tackle the bracken first before placing polythene sheeting over?
PS: I think I have controlled the little bit of knotweed!

Thanks peoples.