How bad does it look if I asked the director of graduate studies if I can change my program of study from pure to applied math after admission? Although I am primarily interested in studying pure math, for certain personal reasons, I had to ask such a question. What I fear now is the mismatch that'll be noticed between my Personal Statement, where I intend to write about my interests in pure math and this query which clearly exhibits the fact that I have as yet not made up my mind. Even if I re-do my personal statement to reflect an interest in applied math instead of pure math, the fact that I wasn't sure at this terminal stage of the application process might go against me. Is there any way to rectify my mistake?

For reference, this question is with regards to a university in the UK.
Assuming your personal reasons are sound, a polite conversation cannot hurt you. Explain your reasons, and keep an open attitude. It is very common for people to change sub-fields (and fields) after their PhD, or even postdocs, so it will not strike as an big oddity.

Now, if it is possible or not, depends mainly on where does your funding come from; and if the university regulations allow it. This will be brought up in the conversation.

If your reasons for studying applied maths are your desire to clone green dogs, well, it will look bad.