I dont see how you could possibly refer to it as a "British accent". Thats somthing that an american would say, yet a brit himself is saying it? It makes no sense.
Britain, is the collective name for more than one country, and certainly more than one region, each with its own distinct accent. You can not have a "british accent". Being very general, you can say "I have an english accent", "a welsh accent", "a scottish accent" or "an irish accent" But each are so vastly different from each other, there is no way you could combine them all to become "a british accent".
If you had said "They knew by my accent that I was from britain" that would be fine, but you have brought shame upon our great nation through this thread.
You should be banished!