Sorry to be bore (or to sound like a stuck record), but remember any thermal energy radiated by the router will create a deficit if the router is switched off, which will cause the gas heating thermostat (if the heating's switched on) to trip in earlier, hence you use more gas.
I know, nobody has the heating on right now, and I agree that in summer, there's savings to be made.
But during winter, contributions to heating from such things (routers, DVDs & TVs on standby, mobile phones charging, etc etc) can be particularly beneficial as they not only relieve the burden (save fuel) from CH during the day, but they may also take the 'chill' off the house overnight when the CH is usually off, allowing the CH's morning startup time to be delayed a little.