Cryptic Subterranian points to a company that does a conversion of Enfield No. 4 and No. 5 rifles from the obsolete .303 British cartridge to the modern 7.62x39 Russian using single-stack 5- or 10-round AK magazines. Why would you do this? Well, the .303 isn't a real common round anymore, so ammunition for it tends to be on the 'spensive side if you don't handload. Also, the Lee-Enfield bolt action, while very slick and quick, isn't the strongest in the world. It has locking lugs located at the rear of the action, rather than at the front near the breech, so the entire action is stressed when fired tending to cause "stretch" over time. I have a No. 5 Mk I Jungle Carbine which has stretched to the point that the headspacing is unsafe now. Enfield designed the rifle to allow for this. An armorer could reset the headspace by replacing the easily removable bolt head. Unfortunately, mine has stretched to the point that the longest bolt head available isn't long enough. The 7.62x39 round has the same bullet diameter (.311") as the .303, but is much less powerful, and therefore less stressful on the action. Kicks less, too. Here's a picture of one that's been converted:
I currently load the lightweight 125 grain .311" bullets designed for the 7.62x39 round in my .303 brass for that reason (I have four examples of this rifle in my "arsenal" - two of which are actually shootable!), but if I can get that No. 5 rechambered for 7.62x39 with safe headspace, it would turn a wall-hanger into a shootable, fun rifle.
It's a wee bit pricey, though.