I don't know how much high player count usually affects the gameplay as I don't really have internet issues even with thousands of players online.
How much RAM (memory) do you have on your pc? Sometimes RAM might be the issue when it comes to lag.
You can check this from your task manager on your desktop. Press Ctrl + Shift + Esc to launch task manager. Or right click the taskbar and select task manager. You should see how much RAM your pc has when you look at the number/Gt in the task manager. You should be able to see how much RAM your pc is using while you are playing from the task manager as well. For example, you are most likely getting a lot of lag if your computer is using something like 7,8/8Gt RAM while you are playing.
You could also try closing every other app and internet browser on your computer if you are having lag while playing. Allthough this should be obvious, but make sure that your pc is not downloading anything while you play.