My interest in the Gawne family is due to two of my ggg grandfathers (Alexander French and Richard Christian)working on the Kentraugh estate.
I did some checking on Jane Gawne the 1881 census and came up pretty empty. There are ten Jane Gawnes in the 1881 census. Ten were on the on the IOM and one in Lancashire. By eliminating those whose married name was Gawne there are only three (unlikely)candidates, a farmer's daughter in Ballaugh born in 1851, a servant in Braddan born in 1866, and a joiner's daughter in Barrow in Furness born in 1870 on the IOM. There were also three Jane Gawns in Hampshire (But married). Possible explanations are that in 1881, Jane was abroad or already married to someone else.
However the IGI has a Charles Forbes Kidd christened at St. James Paddington October 5 1851, son of Charles Kidd & Sarah Jane.
Also the 1881 census has Charles Kidd age 29 (which is consistent with an autumn 1851 birth), occupation cabman, living at No. 2 Shawlerry in Lambeth, born in Kensington (which is not inconsistent with being christened in Paddington). However he is married to a 24 year old Caroline (born in Germany), with two children Herbert (aged 3 b. Brighton) & Charles (aged 8 b Lambeth).
It is a long shot but Jane could be a second marriage. The census also has his potential parents at 21 Arthur Street, Battersea; Charles & Sarah J.Kidd aged 54 and 51.
Good luck, I hope I'm not sending you on a wild goose chase.