Archaeological views are that equids existed in Britain, around 300,000-400,000 BP, as known from evidence found at places such as Boxgrove and Hoxne. Equids were also in these islands during the late Palaeolithic. However, at some time while Britain was still connected to the Continent of Europe, equids either became extinct here or simply migrated south because of adverse climatic conditions.
During the last Ice Age, Northern Britain was totally glaciated; the South was polar/alpine desert and steppe-tundra. These were difficult conditions for large grazing animals. Sea levels during the glacial period were some 400 feet lower than they are today, so the present British isles were not islands but part of the European land mass; it was possible for wild herds to have followed seasonal grazing, southwards in winter, northwards in summer across the low-lying land-bridge of Doggerland which connected Britain to Europe.
The last Ice Age ended some 10,000 years ago. As the grip of the ice eased, gradually ponies and people would have been able to exist further north. The modern view is that all British ponies descend either from stock that re-colonised the islands, or from domestic stock imported by people, or both - possibly during the Bronze Age, possibly later.
Genetic findings seem to support the notion of a remnant population re-establishing itself:
... ponies appear to be established from an ancient ancestral population, with some rare matrilines maintained within the population to this day. The presence of this node suggests the divergence of the ancestral stock during the periglacial period and that today's British ponies may represent a relic of the expansion of animals following the retreat of the last glacial period rather than more recent introductions in the historical period. (Winton, 2020)
Sea levels would also have been rising all the time as the ice and snow thawed, and the Doggerland was inundated about 8,000 years ago. That certainly resulted in the horse population in Britain being isolated from any continental herds by the North Sea and English Channel. It could only be influenced thereafter by human imports.
At any rate, the original herds from which Fells and other British native ponies descend were to be found in these islands long before the Romans came.