You only need a service charge budget when you are dealing with service charges in advance. Without a budget you will be unable to provide leaseholders with the necessary information to make an advance payment – this would make your life as a property manager very hard indeed.
While you don’t need a service charge budget on a site charged in arrears I always feel it is best to provide one. While you might not be asking the leaseholders to contribute in advance, you are giving them an indication of your plans and intentions. This also gives them plenty of time to financially prepare when the bill arrives.