Incident 1 - 03/09/39 SS Athenia

Chronologically, the first civilian loss of life recorded on the CWGC register is the loss of 65 lives on the SS Athenia, torpedoed on the evening of the day that Britain declared war on Germany.
CWGC lists 64 people as having died on the 3rd or 4th September.  The 65th casualty, Rose Griffin, died on the 17th in the Royal Infirmary at Greenock.
Note that the UK civilians killed were only a part of the total loss of life.
Accounts suggest some people died in the initial torpedo explosion, others during accidents leaving the ship, and some when a lifeboat was over-turned.

This website is an excellent source of information:
http://ahoy.tk-jk.net/macslog/IndextoarticlesaboutPasse.html

Rose Griffin, the 65th casualty, has an interesting story:

http://news.google.com/newspapers?nid=1300&dat=19581121&id=GIVVAAAAIBAJ&sjid=T7MDAAAAIBAJ&pg=6716,3251075

http://news.google.com/newspapers?nid=1300&dat=19581114&id=EoVVAAAAIBAJ&sjid=T7MDAAAAIBAJ&pg=6207,2085680

Mrs Griffin had been injured when she fell down stairs on the ship on Saturday night and was in sick bay unconscious with a broken nose and fractured pelvis, but had been forgotten – crew members returned to the ship to rescue her.