i have the same exact problem here too, my pipes and tank are all lagged but this did not prevent anything from freezing, what i have done is rigged up a infa red lamp above the copper pipes and a regular lamp with 100 watt bulb close enough to the pipes (about two feet) and left them on constantly, we now have the toilet back working and the mains water is slowly seeping back into the house, our outside tap is cracked and leaked a lot but now it is one giant ice waterfall, so gotta sort that out as soon as thaw happens.
just be careful with the lamps make sure you dont have them too close to pipes as this can cause damage too. took about a day to get to dribble status
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