Trafalgar Square (on the left one can see Northumberland House, the Jacobean town house of the Duke of Northumberland, which was demolished in the 1870s).
Lambeth Palace, the residence of the Archbishop of Canterbury
Westminster Bridge. This seems to have been painted soon after the present bridge was opened in 1862 (as one might infer from the pile of stones on the right).
Henry Pether belonged to a family of painters who specialized in moonlit scenes: http://www.avictorian.com/Pether_Family.html