Donny, as a regular flyer I can offer the following;

Legal requirements
There are none. The IOM is within the common travel area and no id is formally required. British Airways operate the route from London City and no ID is needed.

Airline requirements
Herein lies the problem. We have Aer Lingus, Flybe, Easyjet and BA all flying in and out and each operate differently.

I flew to LGW last Friday and needed nothing. Returning from LGW however the airline asked for nothing but LGW security did.
Gatwick North is international and domestic and has no way of separating the passengers. IOM generally flies from Gate 55 and the entry to 55 is security controlled. When you enter the security search area at checkin you photo is taken and at gate 55 the photo is recalled to ensure you haven't swapped your boarding card with anyone else. It was at this security check that I was asked for ID. Normally, the officer is just scanning boarding cards.

The moral seems to be make sure you carry something - just in case.