Thanks everyone for looking, and for what you've found so far. It looks like Parker Road wasn't there in 1901!
It's an extremely messy family story - I'll try to keep it brief.
Her mother was Eliza Middleton b. 1854 Richmond. She was a Nursemaid . On the 1881 census taken 3 April she's a nurse at the Southdown Hotel, Eastbourne. On 23rd May she marries HENRY JAMES ALDRIDGE at Eastbourne Register Office.
Henry James Aldridge is my 2xg grandfather and the black sheep of my family. Changed his name, was with numerous women, fathered lots of children by different women. Changed his name frequently, where he lived and his occupation. In a newspaper report of 1893 (Bournemouth) he is charged with 'neglecting a wife' (Eliza). The court report mentions a daughter (Florence Aldridge, aged 9) and states that from 1881 he and Eliza were to-ing and fro-ing between Bournemouth and Brighton. (He also has a partner of about 7 years living in Brighton with 3 children and another due in Sep 1881!)
I haven't yet found a definite birth registration for Florence, so I can't be sure of her birthplace.
Eliza is on the 1891 census in The Firs Home, Christchurch, Bournemouth with incurable TB.
In 1901 Henry is shown with another woman he calls his wife - and her sister -running tearooms in Woking. On the death certificate where Florence gives the Parker Road address, she states that Eliza is 'the wife of Henry James Aldridge, a Chef from Bournemouth' (how accurate this was is anyone's guess!)
Eliza dies in May 1903, and in September of that year Henry marries the sister of the woman he was living with in Woking in 1903 !
I was hoping that if Florence was at Parker Road in 1901 it would give her place of birth - I've no idea what happened to her while her mother was in hospital all that time, or what happened to her afterwards.
Sorry it's so complicated!