What is this weed/Ivy and how to remove it

cleverduck

Hope someone can help. 

I want to know what is this weed/Ivy and how can I remove it, it’s taking over the area I plant potatoes. I had it last year and just kept pulling it out, thinking it will go away, and this year it’s back. Please see pictures below. 

Dovefromabove

Bird’s Eye, Speedwell, Veronica Persica  ... just keep pulling it out as soon as you see it (and before it flowers and seeds). 

Remember, one year’s seeds make seven  year’s weeds 🙄 

JennyJ

On the plus side, it's not deep-rooted and pulls up easily. I compost it, flowers or no, and if more come up then it's more fodder for the compost.