Probably Calystegia sepium. To get all of it can require spot treatment with herbicide as it regenerates readily from broken roots.

Bindweed. It's nearly impossible to get rid of.

There is an old thread in the Weed forum about getting rid of bindweed. Essentially, it said to make a solution of Roundup, place it in a jar, then stuff the growing end of a bindweed plant into it (as much foliage as the container will hold). Anchor the jar in place so it doesn't tip over, and cover to protect it from rain. Eventually the herbicide will do its work.

I don't have a bindweed problem, so haven't had to resort to this, but it was supposed to be effective.

Thanks for all the replies and suggestions. Its definitely bindweed. This should be fun!