How do I get rid of this plant?

In the corner of my front yard I've got this big plant/bush thing growing.

It once had purple lavender looking things on the end, but I've trimmed it right down and want to get rid of it completely.

Image 1:


Image 2:


Some people have mentioned just pouring bleach on it. I'm yet to try anything and was wondering what the best plan of attack is.

If you look closely you will see some of the roots have buried under the edge of the concrete along the side of the wall pulling it away, I'm not sure how far its gone in other directions so just want it killing somehow

Thanks for reading,
Hope someone is able to give me some advice.

 

It is a Buddleia , best to cut it down to about 6in ,and treat with SBK Brushwood Killer as per directions ..

Dave

 

Thanks for the speedy replies guys, great help

Will get onto it tomorrow when the sun rolls around again.

 

The fresh-looking green leaves around the base look like sycamore and ash seedlings. If you think the buddleia's a nuisance, it will be nothing compared with what those seedlings are planning in a few year's time, so get them out double quick while you've still got the upper hand.

 

^ this

I'm trying this approach on the larger ash tree-lets in my garden