Pipe work in old houses is usually of lead; in modern houses it’s more likely to be copper, or even plastic on the cold water circuit. Plastic won’t fracture due to a freeze-up and there isn’t much risk of it with copper. But if you get a frozen lead pipe, stand by for a burst when it thaws.
When water turns to ice, it expands and this can strain the soft lead sufficiently to split it.
Therefore before you start unfreezing, turn off the appropriate stop-tap, just in case, and open fully the tap or taps served by the pipe. See if you can spot a fracture first and if you do, make a temporary repair. If there’s nothing handier, use something like putty, or even soap, and a tight bandage of insulation tape or rag.
A better method is to slit a piece of hose pipe a few inches longer than the fracture and secure it over the pipe with the type of screw clip used on car hoses, or wire twisted tightly with pliers. The best aid for thawing out is a hand-held hair drier.
Starting at the nearest tap, hold the nozzle of the drier close to the pipe and gradually work backwards from it until water starts to flow. If you haven’t a hair drier, direct a fan heater or a portable radiant electric fire along the pipe, but make sure there’s nothing inflammable in line with the fire and that it isn’t too close to the pipe or wall. And don’t walk away and forget about it.
If making a mess doesn’t matter, pour kettles of boiling water along the pipe-runs until you get results.