If you have the correct birthdate and you think he was born in England then you should be able to find James' birth on FreeBMD (free but not complete) or one of the pay-per-view sites such as FindmyPast.co.uk etc (not Ancestry as they use the FreeBMD records)
You will need to get the reference number for the birth and then go to
http://www.gro.gov.uk/gro/content/certificates/ to order it online (cost 9.25bp)
However, I have checked FREEBMD and there is (so far) no James Edmund b 1882 (it's best to use the day - named month - year convention in fam hist as it can be confusing otherwise to non-americans who would see 1/23/1882 as the 1st of the 23rd month!! Doesn't matter for James but it does for Daisy - was she born in May or July?)
Surely if you know the first child was born in Washington you could get a US cert which would give the mother's maiden name?
ANcestry have the emigration records from England to the US. There are also the Ellis Island and Castle Garden sites for entry into the US
Good hunting