Incise,
Reading your post, you have the tests in London, is that correct?
I doubt you'd make a 1740 departure time out of Gatwick given normal timings (the day usually ends about 1700 ish). If you can't change, have a word when you 'register' first thing in the morning, tell them about it, and ask if you can be in the group who has the ATCO talk last. Whenever I do the ATCO bit, in my last session I always make it clear that people are welcome to leave if/when they have to.
If I may comment; it seems a bit silly to book a flight at that time!