I'm not familiar with red deer, but for comparison, last year there was a terrorist in the US who fired a 223 caliber rifle from concealed locations at civilians. I believe one of them was a child, and that he/she survived due to the low power of the 223 round.
The 223 was designed to wound, and to do so with a flat trajectory and at relatively respectable distances. It was also designed with the fully automatic M16 rifle in mind, so many of its design attributes relate to that weapon system. Some critters would be killed by something that would only wound a human, but unless red deer are very small, say sub 70lb, I'd go for something bigger. And if you're going into the brush, well, you know about deflection.
I just now did a search on red deer and they seem to be relatively similar in size to our whitetail, if not larger, perhaps more like our mule deer. 223 is frowned on for them, as it will likely merely wound them and cause a slow and painful death. In the USA, the flat shooting 243 Winchester is generally viewed as a reasonable minimum for deer, with the 25 caliber 257 Roberts and 250 Savage even better. Others go up to 270 Winchester, then 7mm calibers like 280 Rem, 284 Win, and 7mm Rem Mag, while many many many, including me, see no point in going below 30 caliber unless you're small, female, or have some disability or long term injury or condition. In Pennsylvania, lever action rifles in 30-30 Winchester are very popular. An even better brushbuster is 35 Remington, which is more powerful altogether but sacrifices range for weight. The Marlin 336 is probably the best deal in those calibers.
Now I must admit I'm an armchair hunter who reads the stories of others and thinks he knows something. But I've heard enough that I like to think I can say something helpful.
