Welcome to Rootschat. To answer fairly briefly at this stage, your grandfather seems to have been Douglas Beecroft Hall (rather than Beechcroft). His ancestors are fairly easily traceable from the census back to 1841. His parents were John William Hall, b. Bury, Lancs 1848, d. ? 1898, cotton manufacturer, and Mary Beecroft, b. Hyde, Cheshire 1855, d. between the 1881 census and 1887 when her widower re-married. She was the eldest daughter of Samuel Beecroft, a doctor in Hyde.
Is this enough to be going on with?
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