Every linguistics course I've had put it at 80% latinate. Of course numbers can be slippery -- I've seen estimates of the number of words in English ranging from 600,000 to 1,000,000.
Obviously, most of the very common words are native -- or even hybrids like "because" (though even a lot of the most common words, e.g., parts of the verb "to be" are Germanic but not English -- from the Norse invasions).
That's probably what's bouncing around in my mind, the core vocab. There's a bunch of layers in English. Basic Anglo-Saxon. Influxes from the Danelaw, which have similarities to Old Islandic (and when you get to the northern islands, like the Orkeys and Shetlands, a lot more influence from that source goes on there. A dash, but not a lot of Celt. Then comes the Norman invasion. The grammar simplifies out by tons. Huge amount of borrowing. If you separate the direct latin borrow words from the French, you will see how much English by Chaucer's time is an amalgam of French that had filtered down from up top into the everyday talk - in large part because the upper classes mostly speaking French, and those that dealt with them slipped it into their language. At this time we see the separating of Scots from English, with a large number of words that just don't make it into modern English. Renaissance - huge amount of direct adaptations of Latin. It was a time that men of disctinction were known by how large their vocabularies were, and they swelled them with borrowings from Latin, and some from French and Italian, but mostly Latin. Words from India creep in during the Raj. In the 19th and 20th centuries we see more borrowings from German and Greek, in part for technical reasons...because we needed words and we are shameless at stealing them.
What a dynamic language. Breathtaking in it's layerings and regional developments and borrowings.
Everything you don't want a language to be if you want to keep steady meaning over the centuries.
That's what makes Latin such a wonderful tool. It grows some, because of the need for words to describe modern things, but it's done in a textbook way rather in the chaotic organic way that English does. This is why a person with a reasonable Latin background can still read Caesar and understand it. You try reading Beowulf in the original. Even the Pearl, my favorite religious poem in the English language needs heavy glossing.
The joys of language.