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The Doctor simply assumed that the lone "Metaltron" Dalek in "Dalek" was the last survivor of the Time War because he believed that they had all perished along with the Time Lords. That Dalek was unable to contact any other Daleks in that time period, so it also assumed there were no others. However:

The Dalek Emperor also fell through time just like "Metaltron" and began making new, impure Daleks using human DNA; unlike Metaltron, who landed in 1962, the Dalek Emperor ended up in the far future (a few centuries before the year 200,100). ("Bad Wolf"/"The Parting of the Ways")

The Cult of Skaro was not known to have survived because they were hiding in the void. They appeared in "Army of Ghosts"/"Doomsday") and "Daleks in Manhattan"/"Evolution of the Daleks".

Dalek Caan, a member of the Cult, survived these events and managed to break through the time lock into the Time War, saving Davros. Davros created a short-lived New Dalek Empire that featured only in "The Stolen Earth"/"Journey's End".

A ship containing a trio of Daleks had survived the events with Davros and had gone back in time to 1941. They managed to create a New Paradigm of Daleks, which is the form we still see today. ("Victory of the Daleks", "Asylum of the Daleks")