Ok

1911 Census says that Hilda is working as a confectioner (probably runs a sweet shop). She is called Hilda Lawrence born Doncaster, Yorks - age 49
(Marriage date never found. William and his first wife Jane broke up circa 1890; around 1894 he was declared bankrupt). All four children living at home in Kirby - Gilbert 15 born 1896, Reginald 14, born 1897, both born in London
(Never found birth entries), Dora Mary 13, born 1898 and Caroline 11,born 1900.
Gilbert is a milkman (not Reginald) Sorry. I mistook the name Gilbert for Sidney, sorry again.

Hilda's marital status is as married. There is no mention of William at all. Their living accommodation is Kirby Cross, Kirby le Soken.
If they were not married when Hilda had her sons she would have put her surname as Lawrence I would have thought, and not her single surname. What do you think?

Jane, Williams first wife died in 1903 in Woodford, Essex. She was living with her daughter Mary and grandaughter Winifred in 1901.
