Mains water pipe was frozen outside. This has now been defrosted and we have cold water to the kitchen sink but not anywhere else in the house not even to the toilet.

Then the pipes inside your home are frozen. What temp do you have the home set at? Has this ever happened before?

You still probably have an ice plug somewher in the house piping. When you thawed the pipe, some of the ice moved to another cold spot when the water was back on.