Elizabeth's mother Leah née Zachariah, holds the key to the family history. She came from a large family, with branches in London, Portsea Hampshire, and Bath.
Leah's brother (Elizabeth's uncle) John Zachariah was a wealthy 'owner of property' who lived in Hampstead, London. When he died in 1852, he left £1,300 to each of the children of his late sister Leah: Sophia, Sarah, Jane, Elizabeth, Rose, Hannah and Samuel. When John's wife, Phoebe, died in 1861 she left 19 guineas to Bath Synagogue.
We don't know why Elizabeth and her sisters moved to Bath.
But their maternal uncle John Zachariah, the wealthy property owner who lived in London, is registered as having insurance policies in Bath in the 1820s: 24 Stanhope Street, 2 Chandos Bldgs and 4 Pulteney Street. So perhaps he bought the house in Hanover Street for them. He is listed in the local papers as a visitor to Bath and in June 1834 there is a large sale of French furniture, glass and paintings acquired by John during 'six years residence in France'.