How near is a near miss?

I don't fly very often.

Last week Liz and I landed in East Midlands Airport and we had just crossed the M1 from the east and were about 500m from the end of the runway and very low when the engines powered up to what felt like full throttle and we began a very steep climb and bank right for what felt like about three minutes before leveling off and coming round for another go. The pilot kindly told us that he'd aborted because the runway had a plane on it.

Here's a google map of the area to give an idea of distances.

http://maps.google.co.uk/maps?q=nottingham&oe=utf-8&client=firefox-a&ie=UTF8&split=0&gl=uk&ei=c7ZlSsiTNt6NjAfmxPibAQ&ll=52.827765,-1.32102&spn=0.028834,0.082054&t=h&z=14

Now, I'm curious, does that count as a near miss (1 mile) and is this fairly common to frequent flyers? Do ya'll take this kind of thing in your stride?

I found it a little scary. Much scarier than turbulence.