Here we go then. Where it all began.
The first ever Season of Doctor Who debuted on 23rd November 1963 and finished on 12th September 1964. That's 42 weeks of continuous drama, a punishing schedule that seems phenomenally long compared to even the 25-27 week norm of the 70s. But this is the first lesson we must learn - Doctor Who was a very different beast back then. More akin to an ongoing weekly serial, the stories were not obviously divided into 4 or 6-part stories, and had no clear break between each one. Instead each episode ran directly into the next, with the begining of each recapping a few minutes from the end of the last.
Doctor Who Fandom largely came into being in the mid-1970s, when the programme no longer had individual titles, and so the earlier seasons were compartmentalised into meta-groups, such as the first 4 stories of Season 1 ("An Unearthly Child") or the last 6 ("The Massacre"). I have alternated colours on the charts of these earlier seasons to indicate where these fan-based divisions occurred, but the episodes have their original titles, and it is important to realise that the viewing figures reflected this ongoing "serial" aspect of the show. Unlike today's "Asylum of the Daleks", back in 1964, titles like "The Roof of the World" and "The Sea of Death" gave viewers no clues as to what that week's episode was about, and so they tuned in not because of what to expect ("XXX of the Daleks!") but more because they were still enjoying the show. Thus the viewing figures tend to increase and decrease in a slower fashion to what we are used to today.
There are a few telling points we can see with this first season. Doctor Who has an inauspicious start, with less than 5 million tuning in for the now-acknowledged classic first episode "An Unearthly Child". Another couple of million join in the next few weeks, for the far less cerebral (but more action-oriented) visit to the Stone Age. The viewing figures remain steady as the next two episodes begin the first of the show's most overtly Sci-Fi stories. But then look what happens. The Daleks arrive, and viewing figures rocket to 10 million and above.
The show has more than doubled the viewers of its first episode in only its 7th week. The figures remain in the 8-9 millions until week 24, when they drop off by about a million. But for the rest of 1964 Doctor Who remains a trusted, respected, and enjoyable Science Fiction show that 6 million people are content to watch each week.