For your information, Le Méridien Gallia offers valet parking services which cost €20.00 for the outdoor parking and €40.00 for the indoor parking.
at this link you have some more info...
http://specialoffers.starwoodhotels.com/Excelsiorgallia/transports.htm?IM=SOP_linktransports_LM_1870_IMB
but if you are going to Milan in August you shouldn't have any problem about parking... August is not high season in Milan