I'm not sure he ever rejected Beowulf as English myth.  I think it was written around the 600's in Eastern England at a time when Christianity was new here.  People were a bit ambivalent about their religion, often being nominally Christian but worshipping the 'Old Gods' on the side.  The early Kings of East Anglia certainly did this.  Tales like Beowulf would therefore have been composed within memory of this old mythology as a living religion, and give our only real glimpse of what it was like, and would therefore have to have been central to any attempt to recreate an English Mythology, as had been done in Finland with the Kalevala (which I think is what Tolkien ultimately wanted).  Tolkien used Beowulf to some extent when writing the Hobbit.

Unfortunately there is so very little left of the pre-Norman literature left, and so it can't really supply enough material on it's own.  I've read that almost all the Anglo-Saxon poems surviving came from just four books.  Most of this literature was destroyed in the English Reformation, at the Dissolution of the Monasteries.  Abbeys such as Glastonbury had some of the greatest libraries in Western Europe, and they were almost completely destroyed, the books being torn up for cleaning material, or shipped off to mainland Europe as packing material for bookbinders, (a fragment, sixty lines, of Widsith, an epic probably originally as long as Beowulf, turned up at a bookbinders in Copenhagen in the 19th century from some of this surviving material).  The surviving Norse and early German literature mention many of the characters that crop up in the surviving English texts, and Tolkien used some of these in his mythology.  Most famously of course the names of the Dwarves and of Gandalf from the Hobbit, but also others such Scyld Scaefing who turns up in 'The Lost Road', or of course Frodo himself (once an early Danish King).