Look again at the Thomas of Hales poem. It is clearly English except for some Anglo-Saxon trimmings. Since English was not a written language in 1200 AD anyone wishing to write in English wold have had to use a combination of the two alphabets (and their phonetic conventions) that were around at the time i.e. the Latin alphabet and the Anglo-Saxon alphabet. Hence any poem written in English in 1200 AD would likely be English except for some Anglo-Saxon trimmngs.
Now, there was another poet active in England around 1200 AD whose name is Layamon and his work is very well known. He wrote entirely in Anglo-Saxon, the words, the alphabet, the syle, the works.
So now we have documentary evidence that Anglo-Saxon and English was being spoken side by side in England c 1200. Which rules out Anglo-Saxon evolving into Modern English via Middle English at the same time.
I thank you.