I've read somewhere that the remaining "Romans"(britons and actual ethnic romans) in the island of Britain was slowly defeated by the saxons and the remaining romans who survived fled to the Western part of Britain. I've also heard that what remains of them formed the kingdom of Wales. Is there any truth in this? Did they slowly assimilate themselves with the saxons? What happened to the people who called themselves romans even after Rome abandoned Britannia?
Assimilation: they became the Angles, Saxons, Jutes, Welsh, and other peoples that eventually carved up the island into new kingdoms.
The old version of the story, which you'll find if you pick up a book written in the 19th century (and a lot of older ones from the 20th century) is that the Angles, Saxons, and other invaders from Germany invaded Britain and killed, enslaved, or exiled all the remaining Romans to Wales. That's the version you've heard that you mention in your question.
Historians, about 150 years ago, pieced that story together by reading a few different written accounts of British history from the 8th, 9th, and 10th centuries--all written between 300-500 years after this invasion supposedly took place. The problem is, those histories turned out to not be very accurate--and we know that now thanks to archaeology.
What we've found, from using a variety of scientific tests on people's bones (stable isotope analysis, and studying their DNA), is that the different ethnic groups (Angles, Saxons, Romans, etc) that split up Britain between them after Roman rule collapsed were very artificial groups. The Saxons didn't all come from Saxony, for example--people living in the Saxon kingdoms came from lots of different places, and they all adopted the ethnic identity of "Saxons" later on. You see this in every part of Britain, but especially in what became modern England. And the largest group living in any given place was always local British people--the former subjects of the Roman empire.
So after Roman rule ended, the richest Romans left. But millions stayed behind, and they intermarried with newcomers from Saxony, Scandinavia, etc and together formed new kingdoms, most of which ended up tracing their identities back to the newcomer groups (perhaps because it was cool, in the sixth-century, to identify as a Saxon, Angle, or anything else not-Roman since the Byzantine Romans were busy waging a rather unpopular war on a bunch of parts of the former Western Roman empire--that's Alex Woolf's theory, at least, and I think he's on to something).
Most light-skinned people in Britain today can trace most of their ancestors back to prehistory--the majority of the island's light-skinned population arrived in the Neolithic period, thousands of years before the Romans showed up.
If you want to read more about how the locals adapted to changing life after the collapse of the Roman empire, the best book to start is Robin Fleming, Britain After Rome (2011). For anyone who wants to jump into the nitty gritty of the most recent debates about this topic (particularly migration and population continuity), read Susan Oosthuizen's The Emergence of the English (2019) first.