If you want to make clear that you want a number for an answer, I think you'd have to include the word "number" or something synonymous in your question.
For example, yes, in the question you used in your example, "Which exit should I take on the motorway?", someone might quite reasonably answer, "The Reading exit", or "The exit right after the big gray factory".
If you asked, "What number exit should I take?" or "Which number exit should I take?", then I'd expect someone to reply, "The fourth one" or "Exit number 4."
I don't know any simple way to say you want an ordinal number rather than a cardinal number. You could say, "What is the ordinal number of the exit that I should take?" Depending on who you're speaking to, they may well not know what an ordinal number is. You might end up having to use a very clumsy sentence, like, "What is the ordinal number of the exit that I should take? You know, like first, second, third, whatever?"
Of course if you asked, "What number exit should I take?", and someone said, "exit 3", hopefully you can figure out that that's equivalent to "the third exit". I'm not sure in what context an answer of "three" instead of "third" would be a problem.