According to a story in the Metro today the BBC almost cut the revived series at the height of its popularity back in 2009 due to both Tenant and Davies deciding to leave.
The main concern apparently was that they doubted anyone would be able to fill the role after Tenant left given his enormous popularity with the public which is still there given how he still regularly tops polls as the favourite incarnation of the Doctor.
According to current showrunner Steven Moffat it was Davies himself who, having made his opinion felt numerous times while running the show such as cancelling plans for a Rose Tyler spinoff while also launching Torchwood and The Sarah Jane Adventures, was instrumental in convincing the BBC to keep it on the air.
Given how the 2008 series and 2008-10 specials achieved the show’s highest ever ratings since revival, with 13.10 million tuning in for the 2008 Christmas special that also starred David Morrissey (the only higher rating was the 2007 Christmas special “Voyage of the Damned” with Kylie Minogue), this seems like an odd decision to even contemplate.
Just think, if it weren’t for that we’d never have gotten to see Peter Capaldi steal the show as he has for the last couple of years.