I have a No 4 Mk 1 and love it, what a superb bolt action rifle! With a detachable magazine! Great shooting rifles, hope yours is in action with you now.
I wish sometimes that I had a close family member with a nice collection they would pass on to me. I hope you have a blast with this family treasure! After a good cleaning of course.
My first .303 was stamped 1903. My second was 1944 and looked like yours. I loved those rifles. I could almost shoot as fast as my older brother shooting his Garand. And I could hit better, but that was over 25 years ago. Whenever I tried to reload, the cases would always split. Wish I still had them. They shot factory ammo just fine. Like others said...clean them good. You might never get the patch to stop coming out green. lol. It will still shoot fine. If the bolt won't lock, make sure the end of the bolt is screwed on all the way. I was at the range one time, and some guy couldn't get his to lock up. I took one look at it, pulled the bolt, and spun the end. He was real happy when he could shoot his rifle. Have fun, and be careful of what's beyond your target. The .303 will shoot a long ways.
There's a couple of places on the web that sell surplus parts for them. I ordered a sight and a couple of pieces for the stock of my MKIII that the previous owner butchered to put a scope on it. If you need the website name I can look around for the one I bought the replacement parts for.