Sorry for the delay .
Emma's great grandfather was my 5xGreat grandfather James Broscomb born @ 1708.
There is a record (that I can't find again) of a James Broxham baptised somewhere on Oct 26 1712 who could be the one but there are records of lots of Broxoms etc in Batley & Birstall from 1640. Before that it appears they were Broxups from Blackburn(?) Lancashire.
Your Broscombes were quite a puzzle since many took the name Mcguire. Your 2 witnesses were i'm sure christened Earnest Leonard Broscomb Mcguire and Anna Beatrice Mcguire.
The Mcguires appear to have changed back to using Broscombe in the 1900s