Sod's Law! Within seconds of my last posting, mother-in-law phones up and announces she's found an obituary for Alderman Broomfield.
So here are the new facts:
He was Walter James William Broomfield. There's no date on the cutting, but it must be post-1952. He died aged 78, so he must have been born post-1874 (which makes him a possible later edition of the Walter Broomfield, aged 20, at Dunsford on the 1901 census). His wife was Priscilla (d.1952) who was "licensee of the Wheatsheaf Inn, Gosport Street, Lymington, for some 30 years". He sounds like a pompous old git who just loved being on committees (including the Water Management Committee), was a councillor for Lymington East ward and became Alderman in 1940.
So, my original questions still stand, but I'm now trying to work through the dates. If Nell's lady of the Wheatsheaf was already Mrs Priscilla Broomfield in 1898, then it sounds a bit unlikely that Walter was married at 17 or earlier, yet still lived with Mummy and Daddy 3 years later with no sign of the missus. Also I'm not altogether convinced by the notion of a carpenter, son of a gardener, rising to the dizzy heights of Borough Water Engineer and all-round local bigwig. So I'm starting to think there may have been two Walter Broomfields in the area. Could our bigwig be James's little brother? Cousin?
I'm also stymied my the fact that the borough water engineer in 1911 definitely wasn't married to the licensee of the Wheatsheaf. Hmmm!
H-E-L-P!!!!