British Pathe
http://www.britishpathe.com/
A film archive up until 1970
I can't make direct links but so far I have found
-King George VI funeral procession
-Coronation of 1936 procession back to Buckingham from Westminster
-Elizabeth II Coronation proclamation
-A lot of clips of Elizabeth II coronation
There are preview clips that are free to download, they give a good overview of the event. The quality isn't terrific but it is very interesting.