I actually think it may be worth emailing before results day, or at least in the week between Sunday and Thursday of results (when the uni have your results and are making their final decisions about who if anybody to let in of those who missed their grades etc), letting them know that you would like to change.
This means that if the course you want to change to, has got spaces because people with firms have missed their grades, and you have got the grades for it, then you are in a better position to be moved across.
In general at Leeds which is quite popular across the board it is not that easy to change at this point because a lot of courses are quite tight for spaces. In reality changing may involve doing 1st year and then changing and starting again the year after - not ideal although when you are actually at uni you might think you fancy an extra year of being a student (albeit picking up more debt).
I knew a few people at Leeds who changed course but they had to do it that way, like I say its not ideal but if you really fancy changing and they are stonewalling you saying sorry we are full and its not possible then take electives in the course you want to change to, work hard on them, get to know the tutor who takes them (so he/she thinks you're a keen student) and then towards the end of the semester mention to that tutor that you've really enjoyed the elective and actually want to change course, and ask their advice, they will probably say you have to speak to the admissions tutor for that course about transferring, but the advantage there is you have a tutor from that course who can give you a reference to say yep you're good and you are keen. A lot of students have a 'wobbly moment' between accepting their firm and starting, when they suddenly decide for a week they want to be a lawyer or whatever, and tutors are wary about it being a quick fad.