Why does the nameserver change form at my registrar say that my nameservers don't exist?

There are normally three possible reasons for this:

a

You have not got DNS records on your server set up to point to the IP address

b

You are trying to move, for example, anotherdomain.co.uk to point at ns.domain.co.uk before you have moved domain.co.uk to point at ns.domain.co.uk. You need to move the main domain first because this process registers the nameserver with the relevant top level authority which will allow you to move other domains to your nameservers successfully

c

You are trying to move, for example, a .com domain to point at .co.uk nameservers and the nameservers have not been registered with the .com registry