I've an XP laptop which I'm running an Ubuntu distro inside VirtualBox that is managing a website via Tomcat. After I am within the VM I'm able to access the website with http://localhost:8080/

Things I really should do, though, would be to access the VM localhost from XP. http://vm-computer-name:8080/ is not recognized.

Any assistance is much appreciated.

Obtain the Ip of the guest OS and can get on via that.

Setup your VM to operate a number-only network, then reboot or restart networking to update DHCP. The Ip around the guest will be around in the host.

You may also use bridged network mode, but that will not work once the host is disconnected in the network.