I am struggling to find flight numbers and a booking reference from Murcia Spain to Birmingham International from June 2011. We were delayed over 5 hours in Murcia. I have bank payment reference to BMI Derby and dates but thats it?
Do you have a frequent flyer account with that airline? That would list flight numbers at least?
But otherwise, if there is no reference to the booking PNR or flights on your credit card statement and if you no longer have any emails with your confirmation or eTicket numbers in them, you are pretty much limited to asking the airline to research your old booking.
The airlines maintain booking records for a number of years, but older records are archived and the airline will charge a research fee to find it for you. But as I am guessing you want this information to claim compensation for the delay from that same airline, I doubt they will be real keen to do your research.