Doctor Who finished on the 12th September 1964...and then started up again on the 12th October, just over a month later. In hindsight this is more what we would term a 6-week "mid-season break", but in 1964 this was indeed the start of Doctor Who's second season, which would broadcast continuously for another 39 weeks until July 1965.
As we can see a respectable 8 million viewers begin watching this season, approximately 2 million up from 6 weeks ago, possibly due to advance publicity of the show's return with a three-part Sci-Fi story later to be known collectively as "Planet of Giants" (actually the title of the first part of the story). Of course Week 4 finds 1-2 million more viewers tuning in, and this time the reason is plain to see. Advance publicity, and a Radio Times front cover, proclaim the return of the Daleks.
It is also here that we start to see a common trend in these early years - what could be termed the "historical dip". As the Doctor and his companions swop 22nd Century Earth and the planet Dido for 1st Century Rome, just under a million viewers leave. The same phenomenon can be seen when the show departs the planet Vortis and arrives in 12th Century Palestine - the viewers tail off over the "historical" weeks and then perk up with the next Sci-Fi story. Now this could mean that each time there's something more interesting on the "Other Side" (aka ITV), but it's a bit of a coincidence that this happens every time the TARDIS goes into the Past. It's more likely that a significant percentage of viewers who like Science Fiction in their Doctor Who are tuning out whenever a purely historical adventure airs. In fact the figures above plainly show that viewers almost always drop after the first week of a new story. At this time in its history, Doctor Who is very much a children's show, so it would be interesting to find out if ITV was showing something equally child-friendly in the same time-slot, to entice children over who were bored with the TARDIS's latest trip into the History Books.
This is not of course to say that Doctor Who is failing in the ratings. On the contrary, Season 2 is consistently performing better than Season 1. Apart from a slight dip in the third episode of "The Time Meddler", 8 million viewers are regularly tuning in as "Whomania" continues to ride high.