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.