What is the likely hood of an AAT job progressing to a ACA job?

ACCA
PKF
#1

With a big firm such as GT or PKF, do most of the trainees go onto a ACA/ACCA/CA?

#2

I think you should address this question to HR or training dept at these firms. Also take a look at the ICAEW website which is very comprehensive and shows you all the routes to training to be an ACA.
Similarly, look at the ACCA wbsite.

#3

If you join a big firm and do AAT they tend to put you onto ACA/ACCA afterwards

I know someone with a top 20 firm who has just moved onto ACA