Well since there are now very few Alitalia flights out of MXP, I presume this is going to be LIN. If going between MXP and LIN you certainly need to do both. At LIN, if travelling on internationally on Alitalia (God help you) then you in theory don't need to clear passports, but I can't see BA interlining your bags, so you'd have to go out and in again to recheck your bags. The slow bit is main security at LIN which can be good, can be terrible there (in the morning rush). Customs is a non existent process in most of Europe.