Flybe used to operate BHD - LCY direct until around 2 years ago - the problem with this route was that low fares were never available as with all other BHD routes - the return fare was almost always over £200. With the option of less than half of that to LGW. it was hardly surprising the route was poorly supported.
With the right level of fare and suitable aircraft, this route could work - in fact, VLM took over LCY - JER when Flybe relinquished it so they might be a possible candidate - Euromanx are supposed to take over BHD - IOM on the 10 January - it remains to be seen whether it actually happens!