I think that historical Swedish influenced the old English languages when the Swedes (or Nordic people in general) came to England. Many Swedish words look like an earlier version of an English word. At the same time, German and Swedish grammar are not that different, and lots of vocabulary looks somehow familiar to me (as a native German speaker).
But according to language science, English, Dutch and German belong to the westgermanic part of Germanic languages,while for example Norwegian, Danish, Swedish are of the northgermanic part, so English and German should be closer to each other than German to Swedish / English to Swedish.
It feels different, though