If you pass your test on a 125cc bike, you can ride a "big" bike so long as it's restricted to 33bhp for 2 years.
I think you were refering to Accelerated access which is where you've passed your 125 test, have turned 21, are in your 2 year restricted period, and want to be able to ride any bike unrestricted right away. Thats when you take another test: Accerated Access.(This is done on a "big" bike)
Then of course you have the other route, DAS (Direct Access) for people over 21, wanting direct access to full powered "big" bikes.