First, I am assuming that X Factor is not an adaptation of the Marvel comic book. (Though I am assuming that the producers of said show are paying Marvel for the right to use the name "X Factor.")It is much more expensive to make than X Factor, is aimed at the same target audience, and is not as popular. If it goes toe to toe with X Factor, it will lose.
Second, I'm not convinced that Doctor Who would lose in a head-to-head. Worst case, both shows would take a ratings hit; neither would ascend to the same heights as before.
Third, Doctor Who has ancillary revenue streams that X Factor presumably does not.
I realize that viewing habits are massively different in the UK than they are in the US, due in no small part to the license fee. (I get the impression that multiple televisions are far from the norm that they are here.) But the truth is, unless you force the audience to make a choice, you don't know why they're watching.
Doctor Who can put a hit out on a show. The question is, do the programmers have the brass balls to do it?
What in the hell are you on about? Multiple televisions? As in 1 in each room? Of course they're the norm. If you're talking multi-channel, as in cable, etc. Then with Freeview it's actually much more popular around 90% of people have at least 30 channels, about half of them have hundreds. DVRs are becoming very popular too.
But the main 4 networks get about 85% of the viewing audience.
X-Factor has pretty much everything merch-wise Doctor Who has, plus the music that comes of it. X-Factor regularly is the number 1 show, with ratings as high if not higher than Doctor Who.
Also where do you get the idea that they have an aversion to putting popular programming up against each other? Robin Hood and Primeval have been up against each other (to some extent) over the last 2 months. The soaps (most watch shows in Britain) regularly go up against each other.