The budget must be set and agreed by the full council. Once the budget has been agreed, spending decisions within the budget may be delegated, through a formal process of delegation. The issue is how you set the budget. For example, if you say "Open Spaces £50k" then delegate that to a committee, they may decide to spend all of it on a single vanity project. Whereas, if you break the £50k down into £x for grounds maintenance at site y, £z for repainting the bandstand etc etc, the committee has a shopping list and you are simply delegating the final stage of agreeing payments within the framework previously agreed by the whole council.