Can you please identify this vine?

When we moved in about 3 months ago the bottom of the garden was covered in this vine which was wrapped around all the trees, the fence and everywhere else.
It was so bad that when we took a rotavator to it, the roots/vine in the ground brought the rotavator to a standstill. Eventually we got most of it out but now see that in patches it is starting to grow again.
The rotavator chopped up the roots/vine into small pieces what we were unable to pull out of the ground so loads of small bits and pieces, but we thought we would not see the vine again.
Is there any way that this vine can be eradicated totally by treating it with some poison or similar before it takes over again or should we just pull it up each time it appears.
Only problem with pulling it up is that it has very very long roots/vine that seem to run just under the surface of the veggie garden so we don't want to disturb veggie plants too much.
Thanks for any help.

 

Virginia creeper for sure. Spray emerging growth with a glyphosate based weed killer e.g. Roundup and it should kill it in time.

 

Looks very like Ailanthus to me.:hehe:

 

Still unsure as looked it up and the pictures look different but as I am an amateur possibly I am wrong.
I have posted some updated pictures. Please have another look. Thanks.

 

Thanks. Yep it is very invasive and roots and vines run just under the surface. Your last pictrue clinched it. I just dug deep and found that a chopped up piece fo the vine had started growing again so looks like we will start to see a lot more of it coming up at various places where it has been chopped up over the summer months.

 

We tried pulling it up but it was a mammoth task as the vine and the roots were so intertwined below the surface and it became a never ending job. At the moment we have veggies growing in that patch.
I think that the best option may be to let the stuff grow which will help identify the bigger pieces and then come autumn when veggies are all done, dig up the pieces that are growing, permanently deleting them from the picture. All the other pieces hopefully will have died and turned into compost for next year's veggie crop.
Do yu think that this may be another way fo dealing with it or shoudl be just use something like roundup which will save us digging it up?

 

I'd just like to say that the leaves of the plant in question are clearly pinnate, (leaflets along a central stem).

The leaves on virginia creeper are digitate, ( leaflets growing from a central point), and usually five.


I realise its not much help but I cant see the plant being virginia creeper, in those pictures.

I'm not saying it was not present at some stage, but my guess is the rotavator has damaged some ailanthus roots causing them to sucker.

I think digging them out next autumn is the only answer, failing that it would be a case of growing nothing for a season and treat the suckers with glyphosate in mid to late summer next year.