According to Doctor Who TV, the show almost ended when David Tennant left:
Steven Moffat has revealed that the BBC considered ending Doctor Who after the Tenth Doctor’s run.
Speaking at the Hay Festival, he said: “David owned that role in a spectacular way, gave it an all-new cheeky sexy performance and became a national treasure. And he didn’t do it instantly, he did it over time. So the idea that Doctor Who could go on at all in the absence of David was a huge question.”
“I didn’t realise how many people thought it wouldn’t succeed at all. That was quite terrifying when I found out about it later.
“I think there were plans maybe to consider ending it. It was Russell T Davies saying, you are not allowed to end it.”