When I went to India last year the return flight was delayed overnight due to a faulty windscreen so I claimed under the EU Directive page on Virgin's website and got the maximum refund of about £430. In addition to overnight hotel, food, transport etc.
If you have a look at this Martin Lewis article, you see that the three-hour thing is crucial as that's the minimum length of time for a late arrival, before you can claim. Scroll down to the rules for claiming, No. 4: it's not the length of delay to take-off but the delay in landing that counts.
Flight
So if you're late taking off but land only 2 hours & 55 minutes late you can't claim.
Also in this article is a website called FlightStats which seems to give stats on flight times/arrivals so you maybe able to ascertain exactly how late you arrived.