I did a Bsc and then a BA.
I applied through clearing the second time around though (was a very last minute decision to apply!)
The application was still made through UCAS so you need to write a personal statement etc. again, but just list the qualifications you have (including your existing BA).
The application process is the same as it will have been your first time around.
If the areas are relevant in some way to each other, is a Masters a possibility instead?
For example, I did a teaching degree and then went on to do a social work one. At interview they asked if I wanted to do the Masters instead as my existing degree was 'relevant'. I declined because I wouldn't have felt comfortable doing a Masters when social work was something quite new to me. I did wonder afterwards though if I had made the right decision (curiosity rather than regret though).
As the previous poster said, it's a lot of money -if you received support for tuition fees last time, you may not be entitled to them on the new programme.