This started as a scavanger hunt a long time ago and I thought I should belatedly update it for all those who helped.
This was a search for Kate Philadelphia Gerrard who married Frederick Swales in Aldershot on the 24 April 1905 but who seemingly did not exist before that date. In the 1911 census she gave her place of birth as Brede, Sussex and her age suggested a date around 1878, but there was no one of that name born anywhere near there within a timeframe of a decade or so.
The hunt suggested that one possibility was that she was actually an Philadelphia Gain born in Brede in 1874 (Q3 Rye 2b 9) and that this Philadelphia Gain gave birth to an illegitimate child, Elsie Gain, born in 1897 at 157 Marylebone Road, St Marylebone Female Protection Society.(Q3 Marylebone 1a 594). Elsie seemed to have died in Hastings in 1900 (Q1 Hastings 2b 42a) and it was her death certificate which seems to have confirmed this identification.
Although the certificate was ordered for the name of Elsie Gain, what arrived was a certificate in the name of Elsie Garrard, daughter of Frank Garrard, Private in the 1st Battalion Grenadier Guards. The informant was Emily Geater, present at the death at 2 St Mary Terrace, Bexhill Road St Leonard on Sea. The doctor certifying the death was G Garrard MRCS, now identified as George Garrard, surgeon of Seddlecombe Road, St Leonards.
The vital part, though, was in the margin. "Corrected on the 1st August 1900 ... on production of a Statuatory Declaration made by Philadelphia Gain and Mary Anne Biddle. Name to read Gain and Frank Garrard to read Philadelphia Gain a Domestic Servant".
The clue is Mary Ann Biddle, she was the younger sister of Philadelphia Gain and had married Maurice Percy Biddle, a sergeant in the 3rd Scots Guards. Maurice was a witness to the marriage of Kate Gerrard and Frederick Swales in 1905.
But Garrard not Gerrard? I think that that is an error made by the registrar because of the similarity of the dead girl's name and that of the doctor. I cannot find a Frank Garrard in the Grenadier Guards but I can find a Frank Gerrard in the 1st Battalion. In 1901 he was in Wellington Barracks, Bird Cage Walk, St James Park (RG13 piece 96 folio 91 page

. I can trace his history from his birth in Frome in 1872 through to his rejoining the 1st Battalion Grenadier Guards on the 8th Sep 1914 (claiming 12 years previous service in the Grenadiers) and through the First World War.
Not absolute proof but a very strong probability that Kate Philadelphia Gerrard was Philadelphia Gain, but where did the name Kate come from, and where was she in 1901?
Thanks to all those who helped and found Philadelphia Gain for me.
Robert