Anglo-Saxons loved collecting Roman artefacts, and many were buried with small collections of things they clearly found (especially old coins and beads).

There's also evidence that some antiques were put to practical use. Roman spoons show up at Anglo-Saxon settlements frequently, for example.

And Roman buildings were a great source of materials for recycling. Copper alloy jewelry was melted down and used to make more fashionable objects, iron (often scavenged from Roman buildings) was recycled into tools and weapons, and glass and precious metals (like gold solidi) were melted into new high-status objects.

Anglo-Saxons didn't go for all things Roman, though. They don't seem to have liked living in ruined villas; instead, they stayed in wooden houses and were more likely to bury their dead near ruins than to live there themselves. Kings built new palaces from giant trees, and while they would sometimes include some building materials from Roman ruins in these wooden structures, they didn't try to revive the old elite buildings for their new royal residences.

By the ninth century (when we meet King Ecbert), the relationship with the Roman past had changed a bit, but not in the way the history channel suggests.

After England converted to Christianity, there was a long debate about how closely its churches should be allied to the church in Rome. By the ninth century, the Roman church party had won and entrenched its position, with the consequence that Roman things, especially stone buildings, were making a comeback. Reading and latin education were also on the rise, and churchmen like Bede were digging up everyting they could get their hands on.

Ecbert didn't need to hide his fascination with Rome. His bishop would have approved.

I'm not sure whether it's accurate to have him living in a Roman ruin. I know many kings chose not to do this, but Winchester had been a Roman civic centre, and probably had ruins to live in. The show would, at the very least, be more accurate if more Anglo-Saxon royalty lived in majestic timber halls. Perhaps they thought that would look too viking and confuse the audience, but it makes the Saxons look much more bland and nature-hating than they were.

King Alfred had a taste for Roman design that is discernable in his coinage. In the 880s, he issued a new design penny, possibly to celebrate an alliance with Ceolwulf II of Mercia, known as the 'Two Emperors' penny because it is a direct copy, albeit in silver and much smaller, of a Roman solidus design showing two crowned figures that for some reason was particularly prominent in England.

When his daughter Æthelflæd builds the burh at Stafford during the reconquest of England, it starts producing a style of pottery which is also heavily influenced by Romano-British pottery that was previously produced nearby, and was probably still around in many cases.

See Kings, Currency & Alliances, Dumville and Keynes (eds.) and Carver (2010), Stafford: The Birth of a Borough.

This isn't a particular answer to your question OP, but I think it might be worth its existence.

You might want to check the new BBC series "The Last Kingdom" which premiered two weeks ago, and if you like to read, I urge you to read the novels it's based on: "The Saxon Stories" by Bernard Cornwell.

Both are set in the second half of the 9th century in England, on the height of the Dane's invasion and the reign of Alfred the Great. I mentioned this because I believe it has a more accurate portrail or the life of people in Britain at that time. And the Roman physical legacy in Britain plays a large part in the story especially in the form of fortified urban centers or former fortresses which offered superior fortifications than what the Saxons (and Danes) could built at that time. And most of the elite there certainly knew who the Romans were, they knew the Pope was there and Alfred went to the city when he was a child (true) and even knew latin (not sure). But Alfred promoted education and there were many translation from Latin to English is his reign.

And indeed, people that lived in those urban centers did live in Roman buildings, but I wouldn't call them ruins. They are obivously in bad repair, but they are still a sound structures. Bernard Cornwell take some freedoms with the roman physical legacy, but I believe overall the pictures he makes seems plausible.

Maybe someone who knows of this books and have knowledge about the subject can tell how accurate it is.