Well this comes down to a variety of issues, some linguistic and some modern misunderstandings.

First off though, "modern Scandinavians" encompasses several different languages, and not all of them have the same intelligibility with Old Norse that modern Icelandic has. Indeed the mainland Scandinavian languages are not entirely mutually intelligible with each other. Much less their progenitor from nearly a millennia ago. Icelandic is said to have changed the least in this time, and indeed it does retain mutual intelligibility with Old Norse, however this does not extend to the other Scandinavian languages. I'm going to focus largely on Iceland for this answer.

Languages normally can only retain their complexity in full in isolation, and Iceland was not independent throughout its history, and it has been involved deeply in the affairs of Norway and Denmark since its inception. However despite centuries of foreign rule, Iceland itself was rarely culturally dominated despite being politically subservient to other Scandinavian polities. Despite being ruled by Norway and Denmark for much of its history, there do not seem to have been attempts to dominate Icelandic culture and consequently its language was relatively isolated from other influences. Now this is not to say that there were no strong influences coming from the mainland during this time, but in regards to languages there was relatively little impact on Icelandic from other languages to begin with. Nor did this stop many native Icelandic intellectuals from lamenting the intrusion of foreign words into their tongue, but the level of influence was quite minimal when compared to the radical changes that English has been subjected to throughout its own history.

Iceland was famously ruled by the Allthing in its early history, but this period of home rule was ended when the King of Norway was recognized as the lord of Iceland and the local chiefs and officials received their power from him. However, this was not a case of an outside invasion supplanting the local nobility and imposing outside order. Instead, native Icelandic leaders still remained in charge and in positions of authority, even if their ruler resided across the North Sea. Sverrir Jakobsson attributes this change to the inability of local Icelandic rulers to being able to secure their own safety in the face of competition with their rivals. To guarantee their own security they turned to a more powerful third party to enforce peace, the Norwegian King.

However this implementation of outside rule did not come at the cost of Icelandic native rule and authority. Despite occasional attempts by Denmark to force economic domination and religious policy, Iceland has been relatively free of intrusive foreign rule.

This type of relatively indirect rule was common throughout Icelandic history. While a full accounting of Icelandic history is a little beyond the scope of this question, there was never a time in Icelandic history where outright conquered by a foreign power that then either directly or indirectly forced cultural change. Even if Iceland was not free to make its own way in economic, religious, or political affairs, there does not seem to have been significant interference on Icelandic life and language coming from the continent. So despite its long history of subservience to other nations across the North Sea, there were never movements to suppress or ban Icelandic. This state of affairs kept the Icelandic language from being too influenced by other languages. There's another factor in this linguistic "purity" that I'll touch on after dealing with English a little bit.

This is quite a far cry from the situation in England. The Norman conquest, almost overnight, totally reshaped the English nobility and divorced England from Scandinavia and instead bound it closely to the affairs of the continent, namely France. This opened up English to a flood of new influences, namely French and Latin. England was heavily involved with the rest of Europe and a flood of other languages influencing it in a way the Iceland just never was.

Norman French, Norse, Old French, Latin, and so on all had extensive influence on English vocabulary and language. Modern English derives many words from these languages and not its Germanic roots, however these differences in vocabulary (not to mention spelling and pronunciation) were not as present in the medieval period. This is part of why English today is so different from the English of Chaucer (not to mention the Old English of the Anglo-Saxons) there has been a great deal of inflection of new vocabulary into the English language which supplanted older more Germanic words.

The other great change that happened to English was the Great Vowel Shift, which completely changed how vowels were pronounced and formed in English words. Why this process originated is not fully understood, but once it started it totally changed vowel sounds in English, separating it even more from other Germanic languages

This post by /u/bloodswan might be of some help and goes into more depth than I ever could.

Also of note is that in past several centuries there has been a deliberate move on the behalf of Icelandic speakers to keep their language as free as possible of foreign influences. The movement really achieved popularity and broad support in the 19th century where it was tied together strongly with Icelandic independence movements. Once independence was achieved in the early 20th century, the government endorsed and created several institutions for the study and preservation of Icelandic as a language (recently many of these institutions were merged into one).

Deriving support from a tradition dating back to the mid 19th century at least, Gunnar Karlson attributes it going even further back to the 18th century, this movement was intent on ridding Icelandic of words, largely Danish but also German, that were not Icelandic in origin as a part of stating and elevating Icelandic identity. The impetus for this movement came from the, largely Danish educated, Icelandic literary tradition which had achieved a renewal going alongside the Romantic and nationalist movements of the time. Identifying with their own literary tradition stretching back to Medieval times, these thinkers were proponents of using Icelandic words and forms over foreign influences as a way of establishing Icelandic identity, independent of Danish influence. Many of the modern institutes that focus on language policy and neologisms derive their names and aims from these people such as Jonas Hallgrimsson who was the publisher of an Icelandic language journal, and the earlier Arngrimur Jonsson.

However this is not to say that there are no loan words in Icelandic. Without going into the more recent past and avoiding the 20 year taboo, suffice it to say that these numerous institutions have been very active in creating and re-using words from Icelandic to cover new inventions, ideas, and such.

However, language "purity" is a issue that is quite sensitive in Iceland and receives significant government support. There are no equivalents to this in English. Indeed, efforts at linguistic purity in English almost invariably become tied up in white supremacist movements.

So Icelandic has been able to retain its connection to Old Norse through a lack of foreign influence in the first place, and the more recent movement to actively maintain Iceland's linguistic purity. English by contrast has been far more influenced due to the large amount of foreign influence over the language. This took quite dramatic form with the Norman conquest, but has been an ongoing process for some centuries.

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Sources:

History of Iceland. Gunnar Karlsson

"The Process of State Formation in Medieval Iceland", Sverrir Jakobsson