invasive reed?

HI
can anyone identify the plant pictured below. It seems like a reed, is extremely deep rooted & nigh on impossible to dig out.
It has a thick single root which extends horizontally. it's a real thug that has spread over my allotment. I keep cutting it back to below ground and occasionally manage to get it out with the root.
Any ideas what it is?
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From the left picture, it looks like Arundo Donax, the Spanish Cane. If you are just cutting them down, they will just be there. The roots spread sideways and can go very deep. It could have spread from somewhere else, so quite difficult to control.