Marriage certificate arrived!
24th March 1928. Derby RO. William Vernon 21 years, bachelor, general labourer, 88 Bridge Street Derby, father Charles Allen Vernon, butcher, marries Winifred Vasey, 19 years Spinster, shoe packer, 19 St helen's Street, Derby, father Walter Vasey (deceased) Colliery Deputy. Witnesses George Vernon, Frank Stevens, Mary Vasey.
This is my family. The proof is about as good as it gets - not only the fathers, but William at the same address as in 1911 and 1939, Charles known to be alive, Walter known to be dead, witnesses known - George is William's brother, Frank Stevens is Winifred's half brother, and Mary Vasey is not known yet but may be a sister-in-law.
It's also useful to have the exact ages (not a given for those "of full age"). William's age matches his birth and the 1939, and Winifred's matches that 1911 record in Derby (born Ockbrook) and also that record in Kirkby-in-Ashfield in 1939 with son Joseph 1936. I suspect this is an evacuation and that their landlady was confused about their surname. Winifred doesn't have a remarriage date (which would be usual) to fit the name change.
Joseph had three older siblings but I can't find them in 1939, I suspect they are redacted somewhere - evacuees? He has an odd entry by him on that register - 13/5/49 NR 230/RAA. Anybody have any clue what this means? He'd be coming up to 13.
Once again, thanks very much to everybody who helped.