Hi
If it has reference to Crab Tree on the birth certificate, then that is good because that is where Rose Bank was, in the vicinity of Crabtree Lane, Fulham.
William may have been gardening at Rose Bank?
Adelaide Baillie born Hanwell c. 1836 was down in Newton Abbot in Devon in 1871
https://www.familysearch.org/ark:/61903/1:1:V5T5-1NCSo it's not her in Cambridge, I think it unlikely there would be a third one about. Perhaps Adelaide was just coy about her age, like quite a few ladies.
She is still on the electoral register at the same address for 1876/7 (but not listed in 77/8)
On the 1881 possibility, I have yet to see any other sign of a Harry or Henry Bryant born in Cambridge/Cambridgeshire circa 1862. Given the occupation of Harry Bryant, engine fitter, and the mother's details it might be him. How then did Adelaide pick up the Bryant name?
Yes, location good, Henry Baillie seems to be down in the Cann Hall area in 1891, and later on is in Stratford, then Forest Gate. All places local to me
The newspaper report is in the Herts Guardian, 11 Sep 1852
It's not one I have access to at home
From free OCR text
BUNTINGFORD. Inquest.—On Saturday last, an inquest was held by M. S. Longmore, Esq., deputy coroner, at the Old Bell, Ardeley, touching the death of Helen, daughter of William Baillie, gardener, of Ardeley. The sister of deceased, Adelaide Baillie, said ? about seven in the morning, her sister went to the pond in Sir R. Murray's park for some water; about ten minutes after, witness followed her sister and found her lying in the water; she called out Helen, and deceased waved both her hands but did not speak. Witness then went and fetched her father.....(continues)
It's a sad story.
If you just register with the British Newspaper Archive you get three page views for free (which you can download)
https://www.britishnewspaperarchive.co.uk/account/registerJohn