The Christopher/Charles confusion may arise from the composer's habit of publishing simply as "C. à Beckett Williams". I have scores of 5 Impressions for piano (1915), Impromptu op.16/2 for piano and Hampton Court Suite for piano (1919), all with his name in this way. I also have a piano piece "A Hundred Years Ago" (1927) and a unison song "A Sea Song" (1934) by one Beckett Williams. I had blithely assumed they were one and the same, but looking at the later dates, I'd say perhaps not. A son who decided to drop the "à"? Or just no connection at all?
The librettist of Stanford's operas "Savanarola" and "The Canterbury Pilgrims" was Gilbert A. à Beckett. Is there a connection?
Though à Beckett as a surname (or part of one) is unusual, the à Becketts were something of a literary dynasty in Victorian England and there was a distant family connection with W.S. Gilbert.