I have a similar problem. Called BAEC and they said it will take up to 5 days for my account to update. I am a little different given 580 of my tier points were earned during my membership year and the final 20 were earned the weekend after my membership year ended.
I have however been assured by BA that I have been accepted for Silver and that it will take 5 days to process. My online account still shows Blue.
Out of interest, one of the posts above refers to where to order a Silver package? Can someone point me in the right direction?
I am flying on 28th and I would like to select my seats for free. Lets hope they process this in time.
Moore