Hi
Lambeth and Kew are over 9 miles apart and that's if you take the shorter route crossing the winding and semi looping river Thames on bridges that may not all have been in place in 1844. It would be a longer route if you stayed south of the river in the then Surrey, now all London.
William Hart consistently gives his birthplace as Kew but since he is difficult to find on the 1851 census it may be because he was born illegitimately and he appears in another surname on that census which is why it may be worth researching the details of the Hart family of Kew given on the other post particularly any older daughters.
I will move this post to the main Surrey board
Regards
Valda