A process for the alkylation of a benzene-containing refinery stream such as reformate with light refinery olefins which is capable of achieving high benzene conversion levels operates in a fixed bed of an MWW zeolite catalyst, preferably MCM-22, in single pass mode in the liquid phase at a relatively low to moderate temperatures with pressure maintained at a value adequate to ensure subcritical operation. High levels of benzene conversion with conversions of at least 90% and higher, e.g. 92% or 95% or even higher are achievable. A high octane product is produced, comprising mono-, di- and tri-alkylbenzenes with lesser levels of the tetra-substituted products. By operating with staged olefin injection, the end point of the alkylation product can be maintained at a low value while, at the same time, achieving high levels of benzene and olefin conversion.