This is very interesting . The last record I can find of him in the US is his World War One Draft Registration Card.I've checked the US 1910, 1920 and 1930 census' and he's not showing anywhere in the US in the exact form you gave me. I also can't find him in UK births for 1876/77 which is odd as he's showing as being 4 and being born in Widnes as you say on the 1881 english Census,living at 2, Carlton St, Widnes.That data matches the 1891 census where they are all there at the same address. He's not on the 1901 census with his family, but at 21 Shrewsbury Road, Buildwas with his aunt Mary Beech working as a Gardener but on that census his birthplace was given as Buildwas.
On the 1910 US census I found a Herbert Beach living in 328, 330 San Mateo CA whose listed as being born in England in 1877 and being a building contractor ( which his father John was so he looks possible). He's single. I can't find him on the 1920 or 1930 US Census' though or anyone even vaguely resembling him so the last document I can access is his draft card ,giving his mother in Widnes as his next of kin, an image of which I've added to my photobucket so you can copy it via the link below.
http://s133.photobucket.com/albums/q53/paddydr agon_photos/?action=view¤t=HerbertBeechW W1DraftCard.jpg
He appears to still be unmarried at that point, 42, and I can't find him in the US after the war so unless he returned to the UK ( and I can't find a death for him here) then I'm afraid I'm at a loss as to where he went as his draft card is dated September 1918 so I doubt anything grim happened to him.
If you can think of anything might have missed let me know and I'll look it up for you.