Was I nearly involved in an accident? This is a while ago but it has been bugging me now and then.

On September 11 2011 (yes exactly 10 years after 9/11!) I was flying Easyjet 3467 from London Stansted Airport (STN) to Copenhagen (CPH). Scheduled departure was 18:40 local time but the flight was heavily delayed (around 4 hours as I recall) due to another bizarre incident. 

Anyway, as we were finally sitting in the plane and taxiing, suddenly the pilot announces that he just got info that another airplane had been heading to land just where we were and had only been some 60 seconds away! A lot of passengers seemed to gasp for air and the pilot sounded quite shocked as well. But there was no other explanation added.

Is there a database of such events so I could look up more about what happened?

I found the flight on FlightStats (sign in required) but there were no real info.
No, you were not nearly involved in an accident. 

If the flight crew is ready to go, an Airbus A320 takes about 40-50 seconds from the moment take-off clearance is given until lift-off. As soon as the aircraft is off the runway, the next one can land. On some busy airports, 60 seconds between take-off clearance and the next landing is a daily occurrence.

In 60 seconds, there is a lot that can prevent an accident. For example, ATC could instruct the incoming aircraft to go around should the departing traffic not be ready to take-off. This is quite a normal event which happens every day at busy airports around the world. In such a case, the aircraft ready for take-off would have to wait for the incoming traffic to pass overhead. It sounds like you may have experienced such an event. 

Here is a video of something similar happening in Birmingham.

Since it is a 'normal' event, there is no central database that tracks these issues.