Invasive Plant How To Get Rid Of?

Hi,
See photos, this has been growing in my garden and spreads quite quickly.
What would be the best way to get rid off it. Did lever a fork to get a bit up, quite hard going, roots seem strong and pretty deep.
Thanks.

 

Looks like it could be Carex pendula | pendulous sedge/RHS Gardening , but the top of the plant isn't shown to check the flower stems.

 

Not sure what that is, but if you dont want it, I think its roll up your sleeves time and get digging
<Maybe wait until the ground is softer, its like concrete round here at the moment.

 

OK thanks to both of you for replying