Aren't the British specifically known for their over-enunciated t's? If I say Manhatten or Harry Potter there ain't no t in there, they essentially get skipped. British people actually used to show this scene to me to prove that point:
http://www.youtube.com/watch?v=NzWPCbZIJt8
Just in the first 30 seconds.. Harry's "not at all" or "Harry Potter". Again, in comparison, with a NJ/NY accent I basically say "nod-a-all.
Completely depends on the region. I don't pronounce the t's at all, wheras you replace them with d's.
Also, the word 'the' is completely omitted from every sentence where i live.
Going to the shop becomes 'Going to shop' etc.