The earliest mention of Billy Beldham seems to be in a reference to two players called Beldum (sic) who represented Farnham Cricket Club in its earliest known match at Odiham on Tuesday, 13 August 1782.
There was a Beldham (unspecified) in the Odiham team for two matches against Berkshire in October 1782 , and again in May the following year against Maidenhead.