I have a VirtualBox VM on my computer, the VM is running Windows 7 64bit. I installed Android Studio on that VM. I only have the basic Hello World application. When I try to run
Read this post from virtual box as well and see if it applies to your situation please. :) https://forums.virtualbox.org/viewtopic.php?f=6&t=69076. If this is the case I'm afraid that as you requested there would be no free option, as you may have to go for a software such as VMWare which is license based.
What you could otherwise do is not use Intel HAXM inside your existing VirtualBox. That is by using an Android image that does not need hardware acceleration. This is because it is not possible to run two different emulation stacks on your processor at the same time. So since you are already running Virtual Box it would be better to use an emulator that does not need hardware acceleration. You could refer this post: Can I run an emulator without HAXM in Android Studio? if you like. Cheers
EDIT: phil did you try this? It would seem like the only viable option since VMWare isn't free