I am not an expert, but have shot .303s all my life and regularly shoot 6 examples [ME, LEC, MLE x2, SMLE, No4]. In the past I have certainly had one .303, a MLE, which stretched cases a lot, and led to case separations after a small no. of reloadings; I tried everything but was never happy and then sold it on and became happy. And I've been very lucky ever since then with several other rifles; they vary a lot - and it was not down to headspace but the dimensions of the chamber, I understand. The chamber on your rifle does seem wider than most, from the appearance of your case. Although there is often a bright ring on a fired .303 case about 8mm up from the rim [which is, by the way, the same place where most case separations occur] , the bulge shown in your pic does seem unusually obvious. Even if you just resized the necks, I wonder if you'll start to see case separations. Those aren't catastrophic, by the way, but it is not a reassuring thing to happen on the range and it does require having a .303 broken case extractor with you [ see .303 Clearing Plug, Or Split Case Extractor. ]. My personal preference in your situation would be as follows: I'd sell the rifle back to the dealer I got it from, accepting 25% or so loss, and I'd look for another .303 from a reputable dealer but I'd ask if I can do a range test first, to satisfy myself the rifle is accurate and the cases look OK after firing. I think peace of mind has a lot of value. But as I say that is my personal view; I am quite certain others will disagree, perhaps emphatically.
Rob