It is one of the plants known as bindweed - I think its convulvulus arvensis, but it doesn't matter much, there's only one way to deal with it anyway. Best thing to do is remove all the topgrowth you can see, then, as it regrows, insert bamboo canes wherever you see it appearing at soil level.Let the plant twine up the cane, persuading it if you have to, then spray or paint on glyphosate weedkiller. The cheapest way to buy glyphosate is as a concentrate (not as Round up either) and buy a separate trigger spray to mix it up and apply it with. If you do spray the growth, you'll need some cardboard or something similar to stop the spray drifting onto other plants you want to keep. Unfortunately, you will need to repeat this procedure as soon as it starts growing next year too, so check from May onwards for signs of its growth.

Do not put any of the topgrowth you pull off on a compost heap or in the council garden recycling bin - if you can burn it, fine, otherwise pile it up on a hard surface, wait till its crispy and dead, then bin it.

I had to deal with this today at work all through the acers and a conifer!! Do as bamboo advises!

Horrible stuff! We even have to deal with it occasionally here in the desert, though ours is a smaller-leaved variety.