I got out of a local session at Madrid Barajas (LEMD) around a day ago, and I did not have approach to help me. At the time, Madrid was the hub on the ATC schedule.
To handle these busy airspaces without approach, you need to go back to the basics.
Remember what you were taught while in training. The most important thing to do in this situation is to sequence. The planes need to know what plane they are following.
Speed commands are another important thing to use in this situation. A lot of times, the separation will be low, so you can use speed commands to make the separation what it needs to be. Left/right 360s are another great thing to use in this situations.
If a speed command cannot resolve the spacing issue, simply issue a 360. Do not panic, be confident in yourself. If you use these things that I talked about, it will make your session without approach in a busy airspace much easier.