The short answer: they were very aware of the Roman empire and its past glory.
This questions gets to the problem of "What was England Like in the 9th Century?" If you can answer this question well, you can get an idea of whether the average person would known of Rome, or how much they would have known. I would suggest as a starter looking at a simple chronology like England in the 9th Century. As you can see there were a lot of small kingdoms and lots of wars and invasions. Virtually no literary or historical works are known from the period. The Saxon Chronicle was begun during this period, but not published in any way.
Nevertheless, there are some works, the most extensive being those of the poet Cynewulf. His longest poem, which is actually an adventure story, is Elene, which describes the great battle between the Goths/Huns and the Romans/Franks. The hero of this poem is Constantine, the king of the Romans. Of course, nowadays, we consider Constantine of Britain to be a false emperor, and know that he died before the Huns reached the lands of the Franks. Nevertheless, to Cynewulf and his audience Constantine was the great Emperor of Rome and its people resident in England and Gaul who fought the barbarian Huns and saved England. Here is a translated extract from the poem:
But the king was fear-smitten, awed with terror, as he looked upon the
hostile host, the army of the Huns and Goths, that upon the river's
bank at the boundary of the Roman realm was massing its strength, an
uncounted multitude. The king of the Romans suffered bitter grief of
soul, and hoped not for his kingdom because of his small host; he had
too few warriors, trusty thanes, to encounter the overmight of brave
men in battle.
Later the poem describes how King Constantine of the Romans was converted to Christianity and speaks of Eusebius, "bishop of Rome".
There were actually many Roman cities in England and even in the 8th century "Rome" still existed in England in particular communities containing real colonists descended from actual Romans. So, not only were the people in England aware of Rome, they considered them to be friends and neighbors, even. There is a very interesting book, recently published, which is a micro-study of one such town, called Wasperton. The book is called "Wasperton: A Roman, British and Anglo-Saxon Community in Central England.". As you can read in this book, Latin was still widely being spoken in England in the 8th century among ordinary people. Many people even considered themselves to be actual "Romans" even though they were "temporarily" being ruled by barbarian kings.
Now, you might ask, how could someone consider themself to be a Roman, when their king is a Saxon? The answer is that often the Saxon king was far away and the real leader of the community is a bishop, as was often the case. The bishop speaks Latin, every Sunday you go to mass and hear the Latin, you and your friends speak Latin and British. The king might be Saxon, but he speaks a strange language and is not even a Christian and he lives in a town far away. You and your friends live a Roman life, even though Rome itself has been destroyed and the capital moved to Ravenna.
Latin was the lingua franca of the entire island and it was widely spoken by not just ex-Roman communities like Wasperton, Withington and Viroconium, but in many other areas. This is what Bede wrote in the first sentence of his book on the history of Britain:
At the present time, there are five languages in Britain, just as the
divine law is written in five books, all devoted to seeking out and
setting forth one and the same kind of wisdom, namely the knowledge of
sublime truth and of true sublimity. These are the English, British,
Irish, Pictish, as well as the Latin languages; through the study of
the scriptures, Latin is in general use among them all.
Also, the first line from the Saxon Chronicles:
The island Britain is 800 miles long, and 200 miles broad. And there
are in the island five nations; English, Welsh (or British), Scottish,
Pictish, and Latin.
Thus, not only did everyone in England know of the glory of Rome past, many lived it as fallen and conquered Romans hoping for a restoration.