The ideal way would be to use VLANs.
But, if you don't have equipment that will support VLANs, you may be able to do this via a single network without VLANs.
You can put multiple IPs on a single interface, but normally the router system would notice that both the source and destination for the packets are on the same interface. You will have to disable this, it is called an ICMP redirect. You can disable it on the interface in question by writing "0" to the file
The WAN and the LAN will need to have different IP address blocks, and you will also almost certainly have to disable DHCP on the WAN router, or configure it to only give addresses to the Ubuntu router machine.
You may also run into problems with other broadcast or multicast traffic, but this will probably work for some situations. However, realize that it is a very unusual configuration and is likely to require some futzing to get to work.