"...Enfield mk3..." You mean a No. 1 Mk III? Rear sight on the barrel? Serial number on bolt match the S/N on the receiver?
If you haven't actually bought the thing yet, get proof of good headspace. Thousand of 'em have been assembled out of parts bins with no QC. Not even to ensure the thing is safe to shoot.
Otherwise, before you shoot it, check or have the headspace checked. If the headspace is bad, fixing it is expensive. No. 1 bolt heads are not marked and you need a handful to check with proper headspace gauges (no bits of tape, empty cases, wads of gum, bits of string or even feeler gauges.) until you find one that closes completely(any amount of not closed is ok) on a Go, but not on a No-Go. If it does close on a No-Go you use a Field. If it closes completely on a Field, the headspace is excessive and the rifle is
not safe to shoot with any ammo.
Then you need to slug the barrel. Lee-Enfields can have a barrel groove diameter from .311" to .315" and still be considered ok. Larger than .315" the barrel is shot out. Problem is that factory ammo and bullets for reloading are .311" or .312" with some reasonably priced, larger diameter, cast bullets being available from Montana Bullets.
The cartridge itself(Usually with 174 grain bullets these days. Hornady makes a 150 grain SP that'll put deer and up to elk/moose in the freezer. They make 174 grain match ammo too.) will kill any game in North America including big bears.
General info about the No. 1 is here.
http://www.allaboutenfields.co.nz/smle/
Sporterised No. 1's are running about $500 on the auction sites.
Oh and only a No. 1 is an SMLE.