I was mocked for having an English accent when I first moved to Canada. I was younger than you are, and it was really upsetting. I can't control how I speak! In my case I lost the accent very quickly as a form of self preservation.
I don't recommend mocking them back. If nothing else, it shows you thinking mocking how people talk is a fine thing to do. What's the point of that?
You have two real choices: rise above it, or open up about it. A third not very realistic choice is to make different friends. I mention this in passing, because there are plenty of people who wouldn't be mean to you, you are not stuck with this group of friends.
To rise above it, you just smile. You acknowledge that you don't sound like them. You say things like "living abroad has changed me in lots of ways, mostly all good. The accent is just one part of it." You say "I hear girls love British accents" (or "boys", as appropriate.) You say "Americans think everyone with a British accent is positively brilliant!" In every way you consider your accent a good thing: a marker of your broader world, wider experience, different education. (To be honest, this is the root of the teasing - your friends know this is a lovely thing about you and want to say it isn't so that they feel better. It's like teasing someone for being tall or getting the best marks.) Don't be a snob. Don't put them down. Just enjoy this thing about yourself.
If that feels too brave, and these really are your friends, then open up with them. Don't laugh or smile. Look right at them and say "hey, I can't help how I talk now. My parents took me there and this happened. It's not under my control. Don't bug me about it please."
Your plan to make them feel ashamed is not a good one. You want them to either feel empathetic, and not mock you at all (what with being your friend and all) or to realize that you don't mind what they say about your accent, because you like it. Those are achievable goals.