In London, the eastern part of the city is known as the East End. People in other parts of the city sometimes say that it is "up East". Henry is asking Eliza how she ended up in this part of the city because he knows, from her accent, that she was born in a different part of the city. Lisson Grove is in the north/north-west part of London so she has come quite a long way east from her home.
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.