I haven't studied Anglo-Saxon either, but yes I do believe it is the Germanic parts of English with strong links to Swedish. I do find that the more languages (of a certain group) you know, the more likely you are to spot even the less obvious links. For example, 'light' in Swedish is 'ljus' which is pronounced with a silent 'l'; in Danish (and I think Norwegian) it is 'lys' and in German 'Licht'. Going straight from Swedish to English, it looks quite different, but taking the route via Danish and German it looks much more similar.