There are 25 airport and approach sectors available for control in the simulator:
EGCC, EGKK, EGLL. EGSS. THAMES, EGJJ, EGJB, EGBB, (EGCN), EGFF, EGGD, EGGP, EGHH, EGHI, EGNM, EGNS, EGNT, EGNV,EGNX.
Traffic would be presented for positive control and whilst class G traffic would be interspersed, it would not be controllable.
You could, however, create your own flight plans to simulate class G traffic at lower levels. I often add 'low and slow' traffic from EGNR when I'm working EGGP approach... just add a series of fixes and then 'request on frequency' and you have your broader mix of traffic to accommodate amongst others.