Help getting rid of constant weed growth


about 5 or 6 years ago I started getting the below weed growing underneath a row of conifers we had. I removed these conifers last year and dug the ground through. I’ve since levelled out the area and seeded in as a lawn. The grass is just coming through and so is the weed too. I’ve tried round up on it over the years but it doesn’t seem to remove it. Any ideas what it is and how I can stop it growing. Thank you
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thanks for your reply.
I can’t get down low enough to get it all out. In the past when I’ve really dug down there’s a twiggy root that it’s shooting from but the twiggy root is all over the place.