Budgets (Budget Notification Forms) are required by the Guild for all events or expenditure over £1,000, certain event types, and occasionally for other situations such as merch sales. You can check back in the Google Drive to see what historically has required a budget, but if you're not sure best bet is to ask the Guild in plenty of time.
Events or activities which require a budget will be blocked from submitting expenses until the budget is approved. For example, the Guild won't sign the contract for the ball or raise a Purchase Order for it until after the budget has already been approved. This can be problematic, as the higher the cost, the more members of staff within the Guild that have to approve it, so for big events like the ball, this can take quite some time and will take even longer if one of those members of staff is out of the office for whatever reason.
The thresholds change over time, and we don't know for certain what they are, but from experience they seem to be:
disclaimer that these are entirely based on vibes and could be complete and utter wank
Because of how the process works, it also means that if it gets queried or bounced back, when you resubmit it then has to climb every step of the chain all over again. This means that for an especially large event (like the ball) a budget being bounced back even just once can cause significant delays.