British dictionary?
I think you will find there is no such language as British, and it is therefore an English dictionary. I havn't actually looked this up, because when I went to get the book it said "Oxford English Dictionary" on the front in giant letters, which I took to be authority enough.
On the other hand, when I moved to North Carolina, I was had the following conversation with a nice lady from South Carolina. "Honey, where are you from?" Me.. " I am from Liverpool in the UK" She "Your accent is so lovely and your english is so good, what language do you speak there?" Me.. "well, I am English" She "I know that.." and continued to wait for me to tell her what language we spoke.