Hi There,
Yes I have used .303 British on deer before. I was using a handload with a Hornady 150 grain bullet. Only got a quartering shot, bullet entered just to the side of the breast bone and I recovered it mushroomed under the hide just after the last rib on the right hand side, range was about 75 yards, deer ran about 40 yards away from me of course and downhill

. This is the rifle I used:-
It's a BSA Model E. I have also shot (Red) fox with the .303 this time with Winchester factory ammo. 180 Gr SP white box:-
As you can see the Fox turned his head just as I squeezed the trigger, range was a bout 60 yards and the Fox dropped on the spot

though looking at the damage that 180 grain bullet it's no wonder.
The .303 British cartridge is a good one still. Sorry I didn't have the camera with me for the deer

.