Once you know how to use the right sounds to sound British, now you have to use the right words and phrases. Just like how a retired 60 year old American English speaker does not sound like a 15 year old American teenager, it is partly because of the colloquialisms/slang used.
Take 10 minutes to look at the American English words and their British English counterparts. Try and make some spontaneous sentences using the words to get used to them, what they mean, and when you would use them.
If you have any questions/comments along the way, let me know at firstname.lastname@example.org!