Sorry, but this is not correct. The Roman occupation (which would be better characterized as the Roman province of Britannia) had zero impact on English. The Anglo-Saxons pretty much displaced any Latin from Great Britain when they invaded.
It’s not that Latin had no influence on English, but it came from other sources: 1) indirectly via Romance languages (French, Spanish, and Italian, mainly), 2) from the church, mostly in the form of religious terminology, and 3) direct borrowing by scholars in more recent eras.
The raids didn’t do anything in terms of language influences, but the domination of about half of England did. See the Danelaw for more details.
Note that “onward” means all the way to the present day. And the Noman invasion is overrated in its influence on English. Even if it hadn’t occured, English would have borrowed lots of French. After all, France is one of England’s closest neighbors and neighboring languages are the most common source of borrowed words.
BTW, there’s nothing special or “slutty” about English borrowing words from other languages. All languages do it to varying degrees. Some have done so more than English. And for the last century or so, English has been loaning more words to other languages than it’s been borrowing.