Unfortunately, English ivy can be difficult to completely eradicate, but you can definitely make a big impact even with just manually removing the vines. Start on a day after it rains so the ground is softer and the roots come up easier.  You will want to bag up the vines for the trash or pile them somewhere they can dry out and die so that they won't  resprout.  If you decide to use chemical methods, please read the information on this website. There are 4 attachments at the bottom that will give you detailed instructions on how and what to spray.

https://extension.umd.edu/resource/english-ivy/

I hope this is helpful. Robin