FreeBMD has practically complete coverage of births and marriages around this time - the marriage with Lily Moss on the same page as Ernest Gale is the only one whch shows up, but normally the name in the index should be identical with the one on the cert....

Of course, it's possible that they didn't marry until later - or maybe not at all - and just fibbed on WJ's birth registration. That would make things more complicated!
Cardiff isn't exactly next door to Hereford - the registration district covers principally places in Glamorgan, plus a few in Monmouthshire.
According to his marriage and death certs, Edward Walter was born 1906/07, although we should probably consider a year or two on each side as well. No EW shows up, so was he registered as plain Edward, and then added a middle name later? (Perhaps when he was christened.) In that case the Cardiff birth you found is certainly a possibility.
And this birth might be EW's sister:
Births Mar 1908GALE Elizabeth Susannah
Cardiff 11a 461It's the only possibility I've found so far - and it's also in Cardiff....
Rambler