digging them out plus the runners is the best method or you can use a feed and weed type lawn care product.

Water on "Verdone extra" as a feed probably isn't necessary on a new lawn. VE will kill all weeds but leave the grass unharmed

As Anchorman said, use Verdone. I can highly recommend it when I had lawns I used it once a year on them and found it fantastic. I prided myself that I never really got a weed in my lawn, the odd 1 or 2 I did get I just spot treated them.

Just had a thought, it does seem like I work for the company, I don't, LOL.

Can I ask if its a new lawn was it turf? and if so what were the instructions with it and was it sold weed treated? most new lawns are not fed the first year as the turf has already been fed/ weed treated etc.

Thanks so much for advice. I have tried to pull it up. I will try Verdone.
Also, I wasn't too clear. The lawn is only new to us.
Thanks everyone.