Younggun, I concure with all replies thus far. The .303Brit is certainly ok for deer and will probably work ok for elk / moose.
However, be careful in your choice of firearm as "Whitetaildreamer" says.
A lot of the old Lee Enfields are just about shot out, and need to be carefully checked out for head space. If you can find one look for a No.4 Mark-II, Irish arsenal in unfired condition. I sold a couple of them last year at a gun show. Got them thru Southern Ohio Gun supply about 10 years ago. I still have my old No.4 Mk-1 savage made gun (know as a "Lend-Lease Gun") which shoots like a dream.
Gun luck in your search for an Enfield.

VTgao