ECO should normally disable the air con.
Have a look under the bonnet in each mode. When the air con is running you should see the outer pulley of the air con compressor spinning (there are a couple of cylindrical weights on the end which you can easily see when it's running. In addition, the two auxiliary fans in front of the radiator should be running. If it doesn't run in either mode, it could be that one of the pressure switches has disabled the compressor due to failure of the switch, too low or too high system pressure.
Having established in which mode it's actually running you should feel the high pressure pipework getting hot (pipe between compressor and condenser in front of radiator) and the low pressure side getting cool (upper of the two pipes going back into the passenger compartment).
Next thing to check is that the heating water is being cut off. Go for a reasonable run with maximum cooling selected and then, with the engine still running, check the temperature in the pipes to the heater matrix, which you can see if you remove the trim panel above the driver's feet. These should be cold or, at least, not at coolant temperature. If this is not the case I'd suspect the Heater Bypass Valve.
If none of this bears fruit it's best to get a specialist to look at the actual refrigerant circuit.
Kevin