Flight Plans in the IFPS zone (Europe) require a DLA to be put in when the aircraft is running more than 15 minutes later than it's EOBT.
HOWEVER - Don't (as I've seen done) DLA the plan if the aircraft is running slightly late and is on a CTOT (even if it looks like it'll just miss its -5/+10 minute window there). Liaise with ATC first - that 5 minute delay could change into an hour and we might be doing something in the background to get your flight away.
If you want to depart more than 15 minutes earlier you're meant to cancel and re-file. The problem with this is that your departure clearance is actually issued (from the UK centres anyyway) 20 minutes before EOBT. Cancelling means suspending the clearance until the new plan is in the system. So, from a practical point of view, don't do the above unless you want to go more than 30 minutes earlier than the original EOBT.
Flight Plans can be filed up to a week in advance (used to be 96 hours)