I've broached this subject with an EA bailiff before whilst using minnows as spinning deadbait.
As far as the EA are concerned, minnows are not a species at risk, nor are they a species which are managed or monitored for fishery purposes. If they do not constitute part of managed stocks of fish, then the EA cannot issue a license for you to trap them. However, if you trap them, you will enter into the 'grey area' whereby you are trapping fish without a license (even though minnows are not regarded as part of the fish stocks). Also, the average minnow trap does not constitute a net, a line or electro-fishing apparatus, thereby falling into another of the EA's grey areas. The bailiff conceded that if you were caught using one, there's very little the EA could do, even if it wanted to as the costs of prosecution would outweigh the benefits to the environment.
It's never stopped me from using one, and until I'm told otherwise, I will continue to use one.