The closest language to English is a language called Frisian. That doesn’t do anything for mutual understanding though. I listened to a 13 minute segment of a Frisian writer speaking in West Frisian, and I didn’t get one word. But it had a sort of an English rhythm to it, and like when an English speaker hears Dutch, there is something oddly familiar about it, and you strain your ears to listen to it even though you aren’t getting a word.
There are at least three Frisian languages – North Frisian, Saterland Frisian and West Frisian, all of which are very much mutually unintelligible, although intelligibility studies among the languages have never been done.
West Frisian is the most famous and has ~500,000 speakers in the Netherlands. It has ~56% mutual intelligibility with Dutch. It is probably made up of several different languages as some of the dialects cannot be understood by other Frisians.
Saterland Frisian is spoken only in three towns in Northwestern Germany by 2,000 people.
North Frisian is spoken in several widely divergent dialects on the far northwestern coast of Germany in the Schleswig-Holstein peninsula that connects Germany to Denmark in the far north of Germany. This is divided into five separate widely divergent dialects that may well be separate languages. The lexical similarity between these languages is 65-75%, which is in the range of English and North and West Frisian. I don’t see how they can possibly understand each other with 70% lexical similarity. No two lects are intelligible at that distance.
It is from this area that the Angles, Saxons and Jutes, the three tribes that invaded England in ~600 and eventually created the Anglo-Saxon or English language, came.
There are languages that go by the name Saxon in northern Germany and the Netherlands.
There are divergent dialects of Danish called Jutnish, the most divergent of which, Southeast Jutnish, is absolutely a separate language as Danes can’t make heads or tails of it.
And there are even remains of the Angles. There is a city called Angles in this region, and a Low German dialect called Anglish is spoken there. It is quite different and is not understood outside the city.
English and Frisian have been split for 1,300-1,400 years. Old English as preserved in Beowulf goes back to 900-1,000 CE. There are videos of Beowulf on the Net and you can go give it a listen if you like. A British girlfriend of mine listened to it and claimed to understand a fair amount of it. I listened to 10 minutes of Beowulf and didn’t understand a word. Beowulf shows you what happens to two languages that are split for 1,000 years – there’s literally nothing intelligible left.
Recently, a man learned Old English and went to the Frisian region of the Netherlands and tried to speak to an old Frisian farmer there. Incredibly, they were actually able to communicate!
There are reports of Anglo-Saxon English coming to the Frisian area of the Netherlands, then called Frisia, in the 600’s and 700’s, and they were able to converse with the Frisians there well.
West Frisian and Anglo-Saxon were already different languages, but they were so closely related that they could understand each other.
English as noted above was originally from North Friesland and South Denmark, and North Frisian is actually closer to English than West Frisian is. Not that it does you a lot of good. I listened to 10 minutes of an old woman speaking North Frisian, and I didn’t understand a word.