cold water taps not working?

Last night, including around 3am in the morning, the cold water taps were working ok. Around 0500 they stopped working, no water is coming out of any of them, upstairs or downstairs. All the pipes have lagging around them in the loft, the temperature of the house has been a constant 18 degs plus, there has been no problem with the water system at any time during this cold snap. I have even opened the loft to let some warm air circulate up there.