Nonsense. You have been severely misinformed by that CT rep. (Unless they've recently changed the fit of all their cuts, which is highly unlikely and would be stupid and extremely aggravating as I just placed an order for four shirts.)
Anyway, check out these videos on the Charles Tyrwhitt YouTube channel:
From the slim fit video: "This shirt is slimmer in the chest, waist, and hips than our classic fit shirts."
From the tailored (aka "extra slim") fit video: "Slimmer on the chest, waist, and hips than our slim and classic fit shirts..."
Flyswatter - you're right. Charles Tyrwhitt have not changed the sizes of their shirts, just the way they present the measurements (I had this confirmed by a Charles Tyrwhitt sales rep on email). Instead of giving the actual shirt measurements they now give a "to fit chest" measurement.
You can find the old chest measurements at the link below towards the bottom of the page. The table shows that for the chest measurements the Classic Fit is larger than the Slim Fit which is larger than Extra Slim Fit.
[Full disclaimer: this is my site and I have affiliate links on it. However, I think it's justified to post a link as it directly addresses the questions above and it's probably the only place on the web you can get this information. If people think this is wrong I'll happily remove the link.]