How can I punch faster without boxing equipment?

find something that makes you have to react faster . Akedo martail arts would be great for that on top of your boxing .

stand a mattress against the wall and punch as fast as you can, practice it pal, also go into a pool and punch under water

Just punch air, or “jab.” Do 100 punches, 50 with each hand, until your arms don’t hurt, but not particularly trying to punch straight. After that do 100 as fast and as straight as you can. After that is a breeze for you find something with weight to it, 5lbs or less, and do the 100 punches again (I recommend starting with 2 lbs), and still as fast as your arm can go. It doesn’t need to be a “weight” so to speak, but any object with weight to it (book, paperweight, shoe, etc.). If you don’t have 2 of the objects than do one hand at a time, 50 punches each. After 2lbs becomes a breeze raise it to 5, then 7, etc. Never go up more than 2 or 3 lbs as your joints need to adjust to the weight. This is called resistance training, believe me, after you do your first 100 punches holding 5 lbs in each hand, when you put down those weights your arms feel as light as pencils, and you won’t believe how quick you can move them. The best resistance training, however, is done underwater. Get into a pool or lake neck-deep and do the 100 hundred punches as fast as you can. You will feel immediate results. The great thing about water is that the stronger and faster you punch the more resistance it gives you, so you can probably train for speed with the water method alone an see awesome results. Have Fun.