I have never heard ‘despisable’ used in educated British English. Although I do not accept web or word-processor spelling dictionaries as authorities, they do reflect a view of contemporary usage, and the web browser I am using as I write this (Safari, Mac, UK) underlines it as a misspelling. However, consulting two British printed dictionaries I find both words listed.
Chambers (1993 edition)
despicable adj deserving to be despised…
despise to look down upon with contempt, scorn, hate — adj despisable
Oxford English Dictionary (1928)
despicable…1. to be looked down upon or despised, vile, base, contemptible
despisable…1. to be despised or treated with contempt; contemptible, despicable. Now rare.
The first quoted use of despisable is 1340, whereas that of despicable is 1553.
- The two words have identical meanings.
- ‘despisable’ is the original word that was displaced by ‘despicable’ to the extent that it is now uncommon in educated British use.
Use ‘despicable’. It is perfectly correct and will be much more familiar to your readers as it is much more widely used than ‘despisable’.