must be working, the lee enfield was also rechambered for the 7,62x54R so the magazine will have no problems with the thinner 8x57. why not stay with the 8x57 IR? you have to reload it but I suspect you will do this also with 8x57 IRS.
I have somewhere an articel from the old german hunting journal "Wild und Hund" in an early postwar issue where they reporting that many hunters shot 303 british military ammo in the common 8x57IR drilling that come out of the hiding. they turned down the rim thickness of the 303 but it dont shot very well because of the .311 bullet in a .318 barrel.

max pressure for 303 3200 bar
8x57 IR 2800 bar
8x57IRS 2900 bar