From FreeBMD, there is an Ephraim Rainbow who died in Loughborough in Q2 1935 aged 66 (so presumably born around 1869) and an Ephraim Rainbow (presumably the same one) who married in Loughborough in Q2 1908. This seems a likely candidate to be your Ephraim.
However, there weren't any Ephraim Rainbows born around 1869 -- there were only three born in a potentially relevant period (Q4 1852 in London, Q2 1855 in Bedfordshire (this Ephraim is in my own tree and died as a child) and Q2 1888 in Norfolk).
Overwhelmingly the most likely option is Phineas Ephraim Rainbow born in 1868 in Bedfordshire -- again, he's in my own tree. His mother Jane Rainbow later married John William Harris and the family moved to Loughborough sometime between 1881 and 1891, and he appears (from census records) to have been known as Ephraim rather than as Phineas.
Phineas Ephraim Rainbow was my first cousin three times removed (his mother was the sister of my great-great-grandmother).