This tune is called Westminster Chimes. Here's a little bit about its history.
Paddy Dowding from Hornchurch asked about the origin of clock chimes,
especially the Westminster chime. Making History consulted Viscount Alan
Middleton of the British Horological Institute, and Ranald Clouston, Bells and
Clocks Consultant to the Council for the Care of Churches.
The Westminster chime was originally the Cambridge chime, the chime at Great St
Mary's, Cambridge, where a new clock was installed in 1793. The Revd Dr Joseph
Jowett, a law professor, was asked to compose a chime but it is usually
supposed that the composition was by his pupil, William Crotch (1775-1847).
Crotch was a child prodigy and at the age of 11 was assistant organist at
King's College, Cambridge. The tune of the chime is said to be based on a
phrase from Handel's aria 'I know that my Redeemer Liveth'. In 1859 Lord
Grimthorpe chose Crotch's tune for the new clock and bells in the Palace of
Westminster. These words have also become attached to the chime:
Lord through this hour,
Be Thou our guide
So, by Thy power
No foot shall slide
There are many more chimes. The Whittington chime, for instance, comes from the
Church of St Mary Le Bow, in Cheapside, London. Dick Whittington, running away,
heard the Bow bells and turned back - he eventually served three terms as
London's Lord Mayor. Many churches have their own individual chimes played on
three, four, six or even ten bells. Making History played the distinctive
chimes of Merton College, Oxford, and Magdalen College, Oxford. In the late
nineteenth century town and city halls had chiming clocks installed as a symbol
of civic dignity
Eric Bruton, The Illustrated History of Clocks and Watches (Little, Brown &
Company, 2000) "
"The world's most famous chimes are still a popular favourite. Originally
derived from Handel's Messiah, they were first fitted to the University Church
clock of St. Mary's the Great in Cambridge, England. Via their association with
Big Ben in the Victoria Clock Tower of London's Houses of Parliament, their
fame has spread worldwide."
[This site also has a recording of the tune in MP3 and WAV formats.]