The Roman Empire occupied the province of Britannia (roughly corresponding to modern day England & Wales) for quite some considerable time, and it is very well known that Romans did settle down in this province in large numbers and founded great cities like Londinium, just as they did in the other parts of the Empire.
Then, after the spectacular fall of the Western Roman Empire, Roman Britannia became independent against their will and despite numerous attempts of unification with what was left of Rome, this never happened and Britannia stayed - as an independent Roman state. Then, after having to deal with constant raids from the Picts and other Celtic tribes coming from the north, they started to hire mercenaries from Germany to help them fight against the invaders.
These mercenaries, the most prominent of which were the Anglos and Saxons, were promised land in modern day Kent as payment for their war effort. This quickly backfired and the Germanic tribes flocked into Britannia in masses, something the Romans were completely defenceless against, and soon the former allies would see each other as enemies and fight numerous wars, in almost all of which the Germanic settlers emerged victorious.
From this time in the 5th Century A.D. we also know that one of the last Romans to have ever lived, Ambrosius Aurelianus, led his troups into battle at Mons Badonicus - one of the few battles in which the Romano-Britons scored a victory. This was still no antidote to Germanic expansion in Britannia though and the Romans were quickly driven back to Wales and Cornwall, where they would slowly meet their demise.
And that's the point history goes completely dark in regards to Romano-Britons, at least for me. They didn't manage to hold on to Wales and Cornwall, maybe because Romans weren't initally a majority in these regions so not long after that these territories were in Celtic hands again.
But what happened to the Romans? We never hear about them from this moment on. Were they gradually assimilated into the Germanic cultures? Was there some genocide I don't know of? Were the Romans expelled after the Anglo-Saxon invasions? Why didn't a similar situation as in France occur, where after the fall of Rome the territories were also invaded by Germanic tribes but what emerged was a mix-culture, in essence still Latin? But we don't know of any Latin heritage in post-Roman Britain at all, do we? (Except for that which the French brought with them many centuries later)
Then, after the spectacular fall of the Western Roman Empire, Roman Britannia became independent against their will and despite numerous attempts of unification with what was left of Rome, this never happened and Britannia stayed - as an independent Roman state. Then, after having to deal with constant raids from the Picts and other Celtic tribes coming from the north, they started to hire mercenaries from Germany to help them fight against the invaders.
These mercenaries, the most prominent of which were the Anglos and Saxons, were promised land in modern day Kent as payment for their war effort. This quickly backfired and the Germanic tribes flocked into Britannia in masses, something the Romans were completely defenceless against, and soon the former allies would see each other as enemies and fight numerous wars, in almost all of which the Germanic settlers emerged victorious.
So this is the the problem with trying to see where the Romans went. This is the traditional view of 'history' as written by the Victorians based on a largely unquestioning reading of Gildas and Bede. But that textual narrative stemming from Gildas' de Excidio Britanniae is far more Christian polemic than it is actual history, and indeed stands at odds with the history presented to us through archaeological, linguistic and genetic studies. Gildas' narrative - parroted by Bede - is one that occurs time and again in medieval chronicles: the big scary invader who either comes in to take advantage of, or is sent directly as God's divine wrath against, the sins of the people; usually debauchery and lassitude. For Gildas and Bede, the Saxons were God's punishments unto the Britons, halted only when the Britons rallied behind their bishops. For Wulfstan in the 1000s, the resumption of Viking raids during the reign of Æthelred II was a just punishment for the wanton sinfulness of the English; for Gerald of Wales, the Norman invasion of Wales was necessary to prevent the Welsh penchant for homosexuality; for Regino of Prüm, Magyar raiders were punishment for the complacency and infighting of the Carolingian successors, etc.
Leaving aside the extent to which the dissolution the Western Roman Empire was more of a gradual fragmentation than a sudden catastrophic collapse, and the extent to which Britannia was unwillingly left out of the Empire, the arrival of the English was a far slower and less contentious process. The earliest English likely arrived and settled as foederati while Imperial authority was still intact. While many of the early English did indeed settle Kent, others remained as garrison forces in the areas around Hadrian's Wall, and generally speaking, their pattern of settlement wasn't a case of English pushing steadily West and North from Kent, but rather simultaneous piecemeal settlement with no real overall plan across lowland Britain as a whole.
There's an excellent summation of current literature and scholarship in Oosthuizen's The Emergence of the English (2020), but broadly speaking, the process of English settlement was far from military conquest. While in some cases there definitely were elements of violent takeover, the broad pattern suggests that in most cases, incoming English settlers either integrated into existing Romano-British communities, settled alongside them on more marginal land before jntegrating over time, or simply settled land that had fallen out of use in the 420s and 430s. Indeed, the history of Wessex suggests that many of the instances of violence may have been between rival integrated Anglo-British kingdoms fighting over borders, than targeted English takeover of British lands. While genetic studies of periods as early as the 5th and 6th centuries can be of questionable detail, evidence suggests that the proportion of the population of England that was actually "English" was somewhere around 30-40%, and that while elites may have been English (although evidence from Wessex and the Magonsæte suggest that British elites were integrated into many "English" nobilities), the majority of the rural population remained unchanged, or simply integrated with the incoming English and by-and-large adopted their language and material culture over time.
So what happened to the Romans? Well, evidence suggests that in many cases, they just became 'the English.'