No, a trap wouldn't affect whether the pipe would back up or not, either the pipe's restricted, the drain hose isn't far enough in or there's too much water volume.
Of course, standards dictate that it should have a trap, if nothing else to stop sewer gases from escaping.
Thanks guys just sorted it I had checked in elbow last night quickly and in tube with dishwasher hose
Just gone and ripped it all apart and found this mesh I put in last summer at end of pipe as a deterrent against mice all blocked makes sense
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