Could very damp brick garden wall cause crumbly and powdery patch on interior wall

The garden wall being damp could be the cause,as the damp could be rising through the wall and into the problem area also the air brick is to ventilate under the floor so doubt that's the cause unless waters running into it causing damp to rise.If the garden walls higher than your existing damp that my be the problem and a damp cause may be needed in the wall

Sounds like the damp is definetely penetrating from the outside, you mentioned the plaster behind the radiator and under the window is powdery and crumbly, if i was a betting man i would bet that this area of the wall has been plastered with 'bonding' plaster or a similar backing coat plaster , usually in a pink or brownish colour, it's Notorious for not being waterproof and holds water just like a sponge, it's not meant to be applied to exterior walls within a house, it sounds like it's acting like a wick for any moisture that maybe from outside. If this is the case and the powdery crumbly plaster is about 10-20mm thick and pink or brown, then chop it all out with a hammer and chisel back to brickwork, remove the radiator if needs be - then get a plasterer to re-plaster with sand and cement with waterproof additive, or sand and lime. Then a thin coat of plaster on top as normal.In my experience no extra damp proof course should have to be added.