Ok, here's what happened when I tried to send an email through Telnet, directly to the SMTP server:
$ telnet smtp.xxx.ac.uk 25
Trying xxx.xxx.xxx.xxx...
Connected to smtp.xxx.ac.uk.
Escape character is '^]'.
220 smtp.xxx.ac.uk ESMTP ready; send us your mail, but not your spam.
HELO
250 smtp.xxx.ac.uk Hi [xxx.xxx.xxx.xxx] [xxx.xxx.xxx.xxx]; I am so happy to meet you.
MAIL FROM:
250 , sender OK - how exciting to get mail from you!
RCPT TO:
550 Spamhaus hit - http://www.spamhaus.org/query/bl?ip=xxx.xxx.xxx.xxx
Connection closed by foreign host.
I followed the "Spamhaus" link, and I was directed to a page which said that "This IP range has been identified by Spamhaus as not meeting our policy for IPs which should deliver 'direct-to-mx' mail to PBL users." So it looks like the Uni Exchange server rejects emails from IP ranges which are not identified as being from legitimate ISP SMTP servers (or rather are identified as NOT belonging to them).
So I'm stuffed :-(