I'd try lapping the bore, if theres any rifling left that is, then using cast boolit handloads. If not you may be able to fit a No.1 MkIII SMLE barrel to the action.
The sights would require some careful work to remove and remount on the new barrel.
According to this
The Martini and the SMLE have the same shank threads and diameter.
Its mentioned that during WW2 some Martini Enfields were rebarreled with SMLE barrels.