If it's a sniper model No. 4, you may be looking at north of a thousand bucks, unless you find an auction where no one else knows any more than you do.
Lift the bolt handle and look at the info stamped on the metal ring there, holding the stock and forearm together. If it's not actually made at Enfield Arsenal, it may be from BSA or other contractors or from some foreign producer. Lithgow in Australia made many. Other stamps say where it was used. A Broad Arrow property mark within a U means South Africa. The BA within a big C means Canada. Canada also made some No. 4 rifles at Long Branch arsenal. And some were made by Savage here. Savage examples may be marked as US Property, but were Lend-Lease, although I've seen a photo or two of Merrill's Marauders with British rifles in Burma.
The Pattern 13 and 14 rifles do not use the Lee action: they are Mauser-based.
Any really nice SMLE or No. 4 rifle that hasn't been "sporterized" is worth $300-500, and some may be worth a lot more. If a rifle is stamped FTR, it means Factory Thorough Repair. Some look new. And a bunch of No. 4 MK 2 rifles were imported here about 10 years ago in original factory wrap.
It amazes me that some know more about Moisins than they do about the British .303's.
For hunting, look for Winchester or Norma .303 ammo. Remington makes it, but has a RN bullet that may not feed as well in some rifles and may not shoot as closely to the sights. Don't buy .303 Savage ammo by mistake, if you ever find any. It's a different round, more like a .30-30, for Savage M-99 rifles.
There were also British sporting rifles made originally on this action. Some were by BSA, LSA, even by Holland & Holland. They look NOTHING like the ones done here by Bubba. In between are the restocked ones from Parker-Hale. I saw those for about $150-250 at Hudson's Bay Co. in Canada many years ago. They were the best buy I ever saw in an inexpensive hunting rifle. Canadians routinely shoot moose and elk with .303's. In Africa, they've taken elephant, although hardly ideal, especially in thick bush.
And I think the military .303's are among the most historically interesting of any foreign service rifles. Most seen here are in pretty worn shape, but a good one is a really nice rifle. I'd rather be armed with a No. 4 than a Springfield '03.
BE AWARE THAT THE STOCKS come in different lengths. Look at the heel of the stock for a letter code. S=Short, B=Bantam, L=Long. I forgot whether N or R =Regular. See that the stock fits you right. Of course, you may want the rifle, anyway, to re-sell.
The info stamped under the bolt handle will tell you the year made and the Monarch on the throne then. GR=George Rex, either George V or VI. VR= Victoria Regina. ER=Elizabeth II Regina. I guess ER would also mean Edward Rex if made during the fairly brief reign of King Ed.VII.
If you get it, post pics and any stamped data and we'll tell you what you have. Be aware that Australia never made the No. 4 rifle, but some were shipped there, and I've seen a photo of a RAAF man armed with one.
