Pete has a very different shirt than Alex and the other droogs. For one, it has no collar. This is no big deal, except that the only shirts you are going to find with no collar are probably going to be in some formal shop or in the bargain bucket at JC Penney's and is going to be made out of sateen or some shit.
His material is clearly poplin cotton, is thick, well-worn and soft, not thin and painfully sharp like the type of shirt you will find in a mall.
So what is the shirt? Well, it is could be custom, but I think I've found the shirt, or at least the inspiration for the shirt.
It looks like a German M43 heer shirt from WWII. I am fairly confident because a) I counted the buttons b) the style and thickness or the collar and the area where the shirt is buttoned look very similar to Pete's. c) this would go along well with his military themedboots and suspenders (and would be ironic, considering he would be wearing a German shirt, British suspenders, and American boots, and a French beret, thereby showing that his historical perspective is weak or at least his rage is just an outlet for his youthful angst, and his military inspired outfit is just for show. Notice Billy Boy and his gang have military inspired clothing, so it is not surprising that Alex and the droogies would have military clothes.
Here is the shirt I purchased - it was about $60 shipped from a reenactment seller called Spearhead. I had to purchase a reproduction due to difficulty finding an original and, most likely, the prohibitive cost. Depending on the look of the shirt (it is slightly off-white), I will probably stain the pants I get in a Coca Cola solution to match the shirt and the grungy look of the droogs.
Pete unbuttons his long-sleeved shirt and wears a regular cotton collared undershirt. Thankfully, this is much easier to find =)