How to prevent a boiler condensate pipe from freezing
To help prevent your condensate pipe freezing, you can lag the pipe with waterproof and weatherproof lagging.
As a temporary measure, it may help to turn the boiler thermostat (not the room thermostat) to maximum and run the boiler in ‘continuous’ mode, turning the room thermostat to 15°C at night. Turn back to the normal settings once the cold spell is over.
In the longer term, in order to prevent the pipe freezing, you can ask your Gas Safe registered installer to move the pipe so that it runs internally. Or, you could ask them fit a wider pipe, lag it to reduce the risk of freezing, install a trace heater along the pipe which warms it slightly when temperatures drop to freezing, or a combination of all of these.