Most of the reports would probably be of the same league as the ones exemplified by Vallee as "Sergeant Brown has reported a strange light". Others would be standard debrief forms from the '60s and the '70s for military pilots. Others still will be analysis of radar records, soil analysis and so on.
There will surely be no documents saying "Aliens from the planet Omicron Persei VIII landed near a small village in Lincolnshire".
The late Dr Hynek explained very well the apparently tedious nature of these reports to his young and overeager associates. It's bureaucracy. When Sergeant Brown reports to his C.O. about seeing a strange light in the sky, the C.O. will just follow the standing procedure. He will fill the proper form and send it to the proper address where it will be examined, given a protocol number and carefully filed. It's not up to a simple captain or clerk to decide if Sergeant Brown's report can be simply discarded. That's how a tremendous amount of paperwork has accumulated around the world (don't think it's just the M.O.D.).