Paddington was located in London.
A tag on the Seventh Doctor's umbrella read, "If lost please return to Portland Street Library, Paddington, London". (PROSE: Just War [+]Lance Parkin, Virgin New Adventures (Virgin Books, 1996).)
According to one account, Ian Chesterton lived in Paddington. (PROSE: Doctor Who in an Exciting Adventure with the Daleks [+]David Whitaker, adapted from The Daleks (Terry Nation), Target novelisations (Frederick Muller Ltd, 1964).)