Willowfly
I don't recall the incident or work for BMI, so I'm afraid I can't shed any specifics on what happened, but from what you describe, I'd agree with byalphaindia. It sounds very much like an engine surge (when the airflow into an engine is disrupted, causing it to cough, splutter and send impressive - but pretty harmless - jets of flame out of the tailpipe). Either that or one of the engines sucked in a bird, which would also disrupt the airflow, but could cause serious damage to the engine - not to mention the bird.
Hopefully some general points will help allay your fears. Modern airliners are incredibly reliable, and most pilots go years if not decades without ever having to shut an engine down 'for real.' Most captains I know have only had one or two engine failures in careers that span twenty or thirty years. However - and partly because it's such a rare event - we practise engine failures incessantly during our simulator sessions (every six months). And for good measure, before every departure the pilot flying the aircraft will brief the non-flying pilot on what he will do in the event of an engine failure before or after take-off, so the drills are always fresh in our minds. Rest assured then that we spend our whole careers training and being tested for an event that may never happen - but, if it ever does, our actions will be very well rehearsed.
Another point that many passengers don't realise is that all airliners are designed to safely cope with an engine failure during take-off. Each time we fly, we calculate certain speeds, one of which is the take-off decision speed (known as V1). If an engine fails while we are on the runway but before reaching V1, we can safely stop the aircraft on the remaining length of runway. Once passed V1, we are committed to flying. If an engine fails now (as happened on your flight) the remaining engine(s) have enough performance that we can safely continue with the take-off, accelerating to a safe speed and climbing away to a safe altitude. Safety underpins the whole system, and it works very, very well.
Needless to say, an engine failure after V1 means that the pilots will be extremely busy for a few minutes - flying the aircraft, securing the failed engine, talking to air traffic control and briefing the actions that will follow. Inevitably there will be a delay in speaking to the passengers, but flying the aircraft will always take precedence over communicating with the pax (or even ATC). We are, however, well aware that this sort of event will be quite distressing for many of the passengers, and a briefing will be given as soon as possible.
Looking at the odds, you're extremely unlikely to ever experience another engine failure, but if you do, at least you should have a better idea what's going on!
Please enjoy your flying - us pilots do!