You need to ensure that all device connected to your network have different IP addresses. Your BT router will have an IP address & so will your Belkin wifi as will your Desktop & laptop. These all need to be different. I suspect that your desktop & your laptop will be set to DHCP, Which basically means that they will pick up an IP address automatically from a DHCP server, This will be your ISP's servers or even your BT router.
The Belkin wifi may have the same IP address set as your BT router, you need to change this in the Belkin configuration (see the manual). You need to make sure that they are also using the same sub-net mask. This would normally be 255.255.255.0 for a home style network. The BT router may have an IP similar to this: 192.168.254.254 or 192.168.0.254. In this case I would set the Belkins IP address to 192.168.254.250 or 192.168.0.250
Hope this is of some help.