In your Moodle config.php file:
$CFG->wwwroot = 'http://moodle24.olchs.lancs.sch.uk/moodle';
no trailing slash.
Access the server via browser now via moodle24.olchs.lancs.sch.uk ... not the Windows network/shortcut.
a CNAME record is an alias. Would advise an A record for the moodle.
If running Moodle on a Windows server, can the Moodle Windows server lookup the private IP address of the Moodle server (ie, itself) ... by FQDN? Is your Windows Moodle Server pointed to use the internal DNS server first, then outside DNS resolvers?
Might have to flush the DNS cache on the Moodle Windows server - as well as all workstations.
Windows has a (catch 22) fall back for DNS lookups ... it first checks local DNS servers - and in the order they are in config of networking. Assume you have all of your workstations/internal servers pointed to your internal DNS server first: 172.17.32.10). If NONE of those respond, Windows falls back to 'root hints' which then accesses the top level domain servers (in your case the .uk domain) and then works it's way down from there .uk, to .sch, then to .lancs and finally olchs. If it does that, what the station/server will pull/cache is the OUTSIDE DNS IP address.
After making a FQDN entry in your internal DNS, did you reload the zone?
'spirit of sharing', Ken