Within the University of Cambridge, the Computing Service acts as an agent for Thawte and is able to locally administer certificates for computers with hostnames in cam.ac.uk. See http://www.cam.ac.uk/cs/tlscerts/
There are many Certification Authorities available; two of the most well known are
BT (the UK agent for Verisign; formerly BT Trustwise and BT Ignite): http://www.btglobalservices.com/en/products/trustservices/
Thawte: http://www.thawte.com/, now a Verisign brand.
UKERNA (the people who run JANET) have negotiated a reduced-price deal for TLS server certificates from Globalsign. See http://www.ja.net/CERT/certificates/ and http://www.globalsign.net. There were originally some "issues" with these certificates - for details see http://www-uxsup.csx.cam.ac.uk/~jw35/docs/globalsign.html - though they may now have been resolved.