The root cause of the DNS problems is that “they” (for some value of “they”) have changed not only the entry giving the address for sotadata.org.uk, but also the identity of the name servers for the domain.
The address record has a TTL of 3600, so you would expect it to propagate within an hour - perfectly reasonable.
But the NS record is being served from the parent zone org.uk with a TTL of 172800, which is 2 days. The old nameservers are still serving the old address records (or at least one of them is - the other appears to be down). It is quite legitimate to carry on using these servers until the TTL of the NS record obtained from the parent expires.
I would therefore expect this to take up to 2 days plus 1 hour from the time of the original change to sort itself out. In the meantime, some people will get the old address, some will get the new. (Not counting any additional client-side caching outwith the DNS protocol proper).
Doing a DNS change by changing the identity of the name servers is not a clever way to do it Changing address records is routine; changing the nameservers themselves is not something to do lightly.