I have an Intel Core Duo i3-2100 running a flavour of Debian.
I understand Virtual Box is x86-only so is there any similar open source Virtualisation environment that can host images like VMware player on a Windows platform?
VirtualBox will work on a 64-bit Linux host, and is able to virtualize both 32-bit and 64-bit clients as long as you enable the 64-bit client in BIOS.
VirtualBox x86 only ?
You didn't even check the virtualbox website did you ? That was many years ago.
These days you can even run a x64 guest on a x86 host as long as the host supports VT. (Which almost all modern CPU's do.)