When is “L” doubled?
If I am using the word model in the context of financial models and the UK, then which of these words should I use? Also, are there any key difference in the meanings of the two?
There is no difference in meaning. The single-L spelling is more common in the United States; the double-L spelling is more common in the United Kingdom, Australia, South Africa and New Zealand. I don't know which is more common in other countries.
More detail is available at http://en.wikipedia.org/wiki/American_and_British_English_spelling_differences#Doubled_in_British_English
No, there is no difference between them. Modelling is the more common spelling in the UK, while modeling is the more common spelling in the US. Canada tends to use modelling, as do some Americans.