If you were running a café, and trying to keep the health inspectors happy, you should cook and eat the meat by the 3rd.
However health inspectors work to extremely rigid rules, which fail to allow (for example) for differences in storage and cooking methods. Bacteria (even the 'nasty' ones) aren't directly hazardous to your health; it's their waste products that can be toxic. If you waited to until the 4th before cooking the meat, the bacteria would be multiplying (and producing toxic waste products) for a day beyond the (theoretical and probably over-cautious) 'safe' date, so there would be a possible (but slight) risk to your health. If you cook the meat on the 3rd, you'll destroy the bacteria, leaving only the toxic waste products that they'd produced up until then. While the meat is kept in a fridge (at below 4C) for an extra day there will be hardly any bacteria present, so the levels of toxins won't rise beyond the levels that they were at on the 3rd (as they would if the meat had remained uncooked).
'Use by' dates always err on the side of caution. As long as you got the meat home, and into a fridge at below 4C, quickly you can probably safely leave it uncooked until the 4th, and put the cold meat into your sandwiches for several days after that.
When I was a child there were no 'use by' dates and we didn't have a refrigerator. My mother would often keep meat cool in the larder for a couple of days after buying it, before cooking it. She'd then use the cold meat, for sandwiches, for nearly a week after that. Nobody ever got food poisoning.
My own fridge packed up a couple of years ago, and I've never bothered replacing it. I keep meat products (both cooked and uncooked) in a similar way to that used by my mother. I'm still alive!
Chris