I assume the following:
1) This router and switch does not have VLAN capabilities, it is "flat"
2) You have another IP range (10.10.x.x) on the same layer 2
If that is the casethen you need someone that can be a router between this networks, be the "default gateway".
1) You can use a PC running windows with a STATIC IP in both networks with the service of "Routing and Remote Access" running.
2) You can use IP Alias for that (goto properties on the network interface --> TCP/IP --> Properties --> Adavanced --> Add (an IP)
3) The default GW should be defined only on the 192.168.1.x interface and should be the thomson ADSL router, on the 10.10.x.x interface you should not have a default GW.
4) All other computers on the 10.10.x.x. computers just define the default GW as that PC.
5) for the 192.168.1.x the default GW should be the thomson ADSL router.
If the configuration of your network is different please let me know
Good luck,
O