Several reasons-1) They were popular in the courts of the Norman and Angevin kings who ruled England, hence the version we know best today, though of Welsh origins, was added to and changed by the Normans (who probably first heard the legends from Breton allies.)
2) Many places that are of importance in the legends, such as Stonehenge, are in England. Of course in the time of Arthur it would not have been in England; the tribe who were in the area around the time the Romans arrived were the Atrebates. Durotriges also lived nearby.
Actually in the Welsh Mabinogion, Arthur doesn't do much fighting of Saxons; he fights other British kings as well as monsters, witches, ogres, magical boards and so on. Half of his retinue are gods--Lwch Leminawg or Llenleawg, Gwynn, Nudd/Lludd etc. And if you scratch the surface, there seems to be a strong Irish link--with Lwch/Llenleag, the possible inception of Lancelot, being the spear carring solar Irish god Lugh, Nudd Nuadha or Nodens, Morgan-Morrighan etc. Even Excalibur, throgh Welsh Caledfwlch, goes back to the sword of an Irish hero--Caladbolg.The legends of the Green Knight is almost identical to Curoi the Druid, only the old Irish tale is bloodier.
There may well have been a real Arthur (the Saxon incursions did stop fora number of years around the time he was supposed to have lived, but his legend is probably the amalgamation of several Dark Age men with similar names, plus possibly a bear god/demi god whose roots may go back to the bronze age (hence the anachronistic and kind of out of place references to Stonehenge.)
Btw, Devon and a few areas around Swindon spoke a celtic language till the 1100's, and there are still many celtic places names in Somerset, Dorset,Wiltshire etc, such as Pimperne, Pennard,Hackpen. Indeed many English are not as 'Anglo-Saxon' as you might think; there were only 200,000 Saxons at absolute maximum, as opposed to 2 million Britons. They were a dominant warrior society, but anywhere between 30-60% of English people have ancestry from pre-Angl0-Saxon people, especially if their family is in the west of England.