The answer is that they didn't. The Latin influence in the language was SECOND HAND, as opposed to the mainland Europeans. The Roman Empire Latin-speaking Britons were supplanted by waves of barbaric tribes who landed from other parts of Northern Europe. Their language was "pre-German". The language in England became Anglo-Saxon. If you read Beowolf in the original, and know German, there are some similarities. We had an expert who showed us the Lord's Prayer in that language, and it starts "Unser Vater", which is nearly the German for "our Father.
The next dramatic change was the invasion of the Normans in 1066. These folks also started with a base similar to the other Germanic tribes who migrated into Norway and Denmark, but they had settled into Normandy and their language mixed with the early French, which was a mixture of the language of the Franks and Latin. It was that language which gave us the Latin component in our language. By 1400, the English evolved to the language in Chaucer's "Canterbury Tales", which can be followed with some assistance with obscure words. One major feature of that time was that the end vowels of words were still pronounced. From that time, the language evolved into what it is today. It was helped by the development of a dictionary, which resolved alternate spellings of words. For example, the 16th Century King was written "Kynge" in letters and documents of that time. Another evolution was the simplificaion of the language. If you look at the Declaration of Independence, there is a large-script "S" which is the "hissing-s" sound. That has disappeared.