The present invention provides a battery separator comprising (a) a nonwoven web of fibers having a mean diameter of about 15 .mu.m or less and (b) a graft polymerized monomer on the surface of the nonwoven web which renders the nonwoven web spontaneously wettable by an alkaline electrolyte, wherein the nonwoven web comprises at least about 60 wt. % of a first polyolefin having a first melting temperature and no more than about 40 wt. % of a second polyolefin having a second melting temperature which is lower than the first melting temperature, the nonwoven web has been subjected to a temperature between the first and second melting temperatures, and the nonwoven web has a thickness of at least about 50 .mu.m. The present invention also provides a battery containing such a battery separator, as well as a method of preparing such a battery separator and battery.