All of your NS records appear to use public IPs.
SOA record is:
Some nameservers have a different soa serial number That can occur because of recent master update (slave have not loaded master zone yet) or the is a problem in DNS.
SOA (Start of Authority) record states that your master (primary) name server is: , but that server is not listed at the parent servers.
SOA serial number is: This not appears to be in the recommended format of YYYYMMDDnn, where 'nn' is the revision. This number must be incremented every time you make a DNS change.
SOA Retry interval is : seconds. This seems too small. (Values about 3600-7200 seconds is good if not using DNS NOTIFY; RFC1912 2.2 recommends a value between 1200 to 43200 seconds (20 minutes to 12 hours)). This value determines how often secondary/slave nameservers check with the master for updates.
SOA Retry interval is : seconds. This seems too small. (Values about 120-7200 seconds is good). The retry value is the amount of time your secondary/slave nameservers will wait to contact the master nameserver again if the last attempt failed.
SOA Expire time is : seconds. This seems too small. (Values 604800 to 2419200 seconds (1-4 weeks) is good). RFC1912 suggests 2-4 weeks. This is how long a secondary/slave nameserver will wait before considering its DNS data stale if it can't reach the primary nameserver.
SOA Expire time is : seconds. This seems too small. (about 300 to 86400 seconds or 5 min - 24 hours is good). RFC2308 suggests a value of 1-3 hours. This value used to determine the default (technically, minimum) TTL (time-to-live) for DNS entries, but now is used for negative caching.
Trace to slcs.ac.uk
lookup slcs.ac.uk at A.ROOT-SERVERS.NET(18.104.22.168) 73 ms
A.ROOT-SERVERS.NET(22.214.171.124) refer to dns1.nic.uk(126.96.36.199)
lookup slcs.ac.uk at dns1.nic.uk(188.8.131.52) 8 ms
dns1.nic.uk(184.108.40.206) refer to dns-3.dfn.de(unknow IP)
extra IP lookup for dns-3.dfn.de at root server A.ROOT-SERVERS.NET(220.127.116.11)
lookup dns-3.dfn.de at A.ROOT-SERVERS.NET(18.104.22.168) 69 ms
A.ROOT-SERVERS.NET(22.214.171.124) refer to a.nic.de(126.96.36.199)
lookup dns-3.dfn.de at a.nic.de(188.8.131.52) 35 ms
a.nic.de(184.108.40.206) refer to dns-3.dfn.de(220.127.116.11)
lookup dns-3.dfn.de at dns-3.dfn.de(18.104.22.168) 93 ms
got A record 'dns-3.dfn.de IN A 22.214.171.124' from dns-3.dfn.de(126.96.36.199)
lookup slcs.ac.uk at dns-3.dfn.de(188.8.131.52) 92 ms
dns-3.dfn.de(184.108.40.206) refer to charm.ns.slcs.ac.uk(220.127.116.11)
lookup slcs.ac.uk at charm.ns.slcs.ac.uk(18.104.22.168) 83 ms
got A record 'slcs.ac.uk IN A 22.214.171.124' from slcs.ac.uk(126.96.36.199)