I believe in theory on a good day with a following wind
Not all airlines have both a 2 letter IATA and 3 letter ICAO designator...each is subject to individual application and operators needs
the IATA 2 letter code is the only one used on a Computer Reservation System which is what travel agents use to sell tickets direct to the public - whether this be 'scheduled' or seat allocations/blocks from charter carriers which are allowed for sale direct to the public (not as part of a package holiday)
the ICAO 3 letter designator is used by ATC and some airports show this on arrival/departure screens as the data is ATC computer based
So if you are a charter carrier and not selling seats on a CRS then you dont need/have an IATA 2 letter code - just the ICAO 3 letter one which in many cases is the only one a carrier will have
Britannia and MyTravel both are allowed to sell some of their seats direct to the public (via CRS or similar) hence possibly use of both and also certainly in the case of Britannia their code was issued many years ago when ATC also used the 2 letter designator in parallel to IATA...in the end ICAO ran out of 2 letter options and had to go to 3