Do it! Book your first lesson and see what it's like.
I'm about 9 hours into my PPL and also have a very slight speech impediment which I thought would be a problem. As it turns out, it isn't. Like with anything in life, you find a way to get around things like that. I found a big breath before I speak on the radio works a treat.
Doing the ATPL is a long term thing (and also expensive) so it might be worth, before you start stumping up £0,000's , to do it over a period of time. Start with the PPL and work it out from there.
You'll do it - You'll love it - Your bank manager won't!!